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font-size: 14.5px; color: var(--muted); }\n\n \/* \u2500\u2500 PYQ TREND BADGE \u2500\u2500 *\/\n .pyq-year {\n display: inline-block;\n background: var(--dark);\n color: var(--accent);\n font-family: 'JetBrains Mono', monospace;\n font-size: 12px;\n font-weight: 600;\n padding: 3px 8px;\n border-radius: 4px;\n margin-right: 6px;\n }\n\n .pyq-item {\n padding: 14px 0;\n border-bottom: 1px solid var(--border);\n }\n\n .pyq-item:last-child { border-bottom: none; }\n\n \/* \u2500\u2500 RESPONSIVE \u2500\u2500 *\/\n @media (max-width: 768px) {\n .section { padding-top: 36px; padding-bottom: 36px; padding-left: 0; padding-right: 0; }\n .cta-section { padding: 44px 0; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"article-body\">\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">01<\/div>\n <h1 class=\"section-title\">Introduction to <span>Motion in a Plane<\/span><\/h1>\n <\/div>\n\n <p>\n Mastering <strong>Motion in a Plane Class 11 notes<\/strong> is essential for every NEET aspirant targeting a top score in Physics. In Class 11 Chapter 4, motion is extended from a single straight line into a two-dimensional coordinate plane \u2014 and this shift demands a completely new set of mathematical tools: <strong>vectors<\/strong>.\n <\/p>\n <p>\n When an object moves along a straight line, a single number with a sign (+\/\u2212) describes its state completely. The moment motion occurs along a curved path \u2014 a ball thrown into the air, a boat crossing a river, a satellite orbiting Earth \u2014 a single scalar number is no longer sufficient. You need both <em>magnitude<\/em> and <em>direction<\/em>, which is exactly what vectors provide.\n <\/p>\n <p>\n This chapter lays the mathematical and conceptual foundation for two of the most important topics in NEET Physics: <strong>projectile motion<\/strong> and <strong>uniform circular motion<\/strong>. Every derivation, every formula, and every numerical problem in this chapter traces back to one core skill \u2014 resolving a vector into its perpendicular components along the x and y axes.\n <\/p>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Why This Chapter Matters for NEET<\/div>\n <p>Motion in a Plane consistently appears in NEET with 2\u20133 direct questions. Projectile motion alone accounts for roughly 1\u20132 questions per year. Strong conceptual clarity here also supports Laws of Motion and Work-Energy chapters.<\/p>\n <\/div>\n <\/div>\n\n <h3>Related Reading<\/h3>\n <div class=\"related-links\">\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/neet-physics-survival-kit-2026\/\" class=\"related-link\">NEET Physics Survival Kit 2026<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/organic-chemistry-strategy-neet\/\" class=\"related-link\">Organic Chemistry Strategy NEET<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/neet-biology-tricks-for-exams\/\" class=\"related-link\">NEET Biology Tricks for Exams<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/score-340-in-neet-biology\/\" class=\"related-link\">How to Score 340+ in NEET Biology<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/top-10-tricky-neet-biology-diagrams\/\" class=\"related-link\">Top 10 Tricky NEET Biology Diagrams<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/free-study-material\/\" class=\"related-link\">Free Study Materials \u2014 KSquare<\/a>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">02<\/div>\n <h2 class=\"section-title\">Scalars and <span>Vectors<\/span><\/h2>\n <\/div>\n\n <p>\n The most fundamental distinction in mechanics is between <strong>scalar<\/strong> and <strong>vector<\/strong> quantities.\n <\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Feature<\/th>\n <th>Scalar<\/th>\n <th>Vector<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Definition<\/td>\n <td>Magnitude only<\/td>\n <td>Magnitude + Direction<\/td>\n <\/tr>\n <tr>\n <td>Examples<\/td>\n <td>Mass, Temperature, Distance, Speed, Energy<\/td>\n <td>Displacement, Velocity, Acceleration, Force<\/td>\n <\/tr>\n <tr>\n <td>Notation<\/td>\n <td>Plain symbol: m, T<\/td>\n <td>Bold or arrow: <strong>A<\/strong>, ⃗A<\/td>\n <\/tr>\n <tr>\n <td>Addition rule<\/td>\n <td>Ordinary algebra<\/td>\n <td>Vector (triangle\/parallelogram) law<\/td>\n <\/tr>\n <tr>\n <td>Negative value<\/td>\n <td>Means smaller\/zero<\/td>\n <td>Means opposite direction<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Warning \u2014 Common Confusion<\/div>\n <p>Speed is scalar; velocity is vector. Distance is scalar; displacement is vector. NEET frequently tests this distinction \u2014 never use them interchangeably.<\/p>\n <\/div>\n <\/div>\n\n \n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/3-mission-180-neet-physics-rankers-batch\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"display:block; margin-top:28px; margin-bottom:8px;\">\n <img decoding=\"async\" src=\"https:\/\/ksquareinstitute.in\/blog\/wp-content\/uploads\/2026\/03\/Course-Poromo-Banner-scaled.png\"\n alt=\"Mission 180 NEET Physics Rankers Batch - KSquare Career Institute\"\n style=\"width:100%; height:auto; border-radius:10px; display:block;\">\n <\/a>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">03<\/div>\n <h2 class=\"section-title\">Vector Representation \u2014 <span>Components & Unit Vectors<\/span><\/h2>\n <\/div>\n\n <p>\n Any vector in a 2D plane can be completely expressed using its <strong>rectangular components<\/strong> along the x-axis and y-axis. This is the most powerful technique in Motion in a Plane Class 11 notes and is used throughout the chapter.\n <\/p>\n\n <h3>Unit Vectors<\/h3>\n <p>\n A unit vector has magnitude exactly equal to 1 and points along a specified direction. The standard unit vectors in 2D are:\n <\/p>\n <ul>\n <li><strong>î<\/strong> \u2014 unit vector along the positive x-axis<\/li>\n <li><strong>ĵ<\/strong> \u2014 unit vector along the positive y-axis<\/li>\n <li><strong>k̂<\/strong> \u2014 unit vector along the positive z-axis (for 3D)<\/li>\n <\/ul>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Vector in Component Form<\/div>\n <p>A = Ax i + Ay j<\/p>\n <p>|A| = √(Ax² + Ay²)<\/p>\n <p>θ = tan⁻¹(Ay \/ Ax) [angle with x-axis]<\/p>\n <\/div>\n\n <p>\n The components Ax = |A| cosθ and Ay = |A| sinθ allow you to separate any 2D problem into two independent 1D problems \u2014 one along x, one along y.\n <\/p>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Tip \u2014 Resolution Strategy<\/div>\n <p>Always choose axes such that maximum vectors lie along one axis. This minimizes the number of components you need to calculate and reduces arithmetic errors.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">04<\/div>\n <h2 class=\"section-title\">Vector Addition and <span>Subtraction<\/span><\/h2>\n <\/div>\n\n <h3>Graphical Methods<\/h3>\n <p>\n <strong>Triangle Law:<\/strong> Place the tail of the second vector at the head of the first. The resultant is drawn from the tail of the first to the head of the second vector.<br>\n <strong>Parallelogram Law:<\/strong> Place both vectors tail-to-tail. The diagonal of the parallelogram formed represents the resultant.\n <\/p>\n\n <h3>Analytical Method (Component Addition)<\/h3>\n <p>This is the method used in all numerical problems. Add corresponding components separately:<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Resultant of Two Vectors A1 and A2<\/div>\n <p>Rx = A1x + A2x<\/p>\n <p>Ry = A1y + A2y<\/p>\n <p>R = √(Rx² + Ry²)<\/p>\n <p>tanθ = Ry \/ Rx<\/p>\n <\/div>\n\n <h3>Vector Subtraction<\/h3>\n <p>\n Subtraction is defined as adding the negative vector. Reversing a vector reverses its direction but keeps the same magnitude:\n <\/p>\n\n <div class=\"formula-orange\">\n <p>A − B = A + (−B)<\/p>\n <p>−B has the same magnitude as B but points in the opposite direction<\/p>\n <\/div>\n\n <p>\n Both graphical and component methods apply. In component form: Rx = Ax − Bx and Ry = Ay − By.\n <\/p>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">05<\/div>\n <h2 class=\"section-title\">Multiplication of Vectors \u2014 <span>Dot & Cross Product<\/span><\/h2>\n <\/div>\n\n <p>\n Two types of vector multiplication appear in Class 11 Physics. Understanding when to use each is critical for NEET.\n <\/p>\n\n <h3>Scalar (Dot) Product<\/h3>\n <p>Produces a scalar result. Measures the projection of one vector along another.<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Dot Product<\/div>\n <p>A \u00b7 B = AB cosθ<\/p>\n <p>W = F \u00b7 d = Fd cosθ [Work is a dot product]<\/p>\n <p>If θ = 90° → A \u00b7 B = 0 (perpendicular vectors)<\/p>\n <p>If θ = 0° → A \u00b7 B = AB (parallel vectors)<\/p>\n <\/div>\n\n <h3>Vector (Cross) Product<\/h3>\n <p>Produces a vector result. The resultant is perpendicular to both original vectors.<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Cross Product<\/div>\n <p>|A × B| = AB sinθ<\/p>\n <p>τ = r × F [Torque is a cross product]<\/p>\n <p>If θ = 0° → |A × B| = 0 (parallel vectors)<\/p>\n <p>If θ = 90° → |A × B| = AB (maximum)<\/p>\n <\/div>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Property<\/th>\n <th>Dot Product<\/th>\n <th>Cross Product<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Result type<\/td>\n <td>Scalar<\/td>\n <td>Vector<\/td>\n <\/tr>\n <tr>\n <td>Formula<\/td>\n <td>AB cosθ<\/td>\n <td>AB sinθ<\/td>\n <\/tr>\n <tr>\n <td>Commutative?<\/td>\n <td>Yes: A\u00b7B = B\u00b7A<\/td>\n <td>No: A×B = −(B×A)<\/td>\n <\/tr>\n <tr>\n <td>Application<\/td>\n <td>Work, Power<\/td>\n <td>Torque, Angular momentum<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">06<\/div>\n <h2 class=\"section-title\">Position, Displacement, and <span>Velocity in a Plane<\/span><\/h2>\n <\/div>\n\n <p>\n The concepts of position, displacement, and velocity are extended into two dimensions by expressing them as vectors using the component form learned earlier.\n <\/p>\n\n <h3>Position Vector<\/h3>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Position & Displacement<\/div>\n <p>r = x i + y j [position vector]<\/p>\n <p>Δr = r₂ − r₁ = (x₂−x₁) i + (y₂−y₁) j [displacement]<\/p>\n <\/div>\n\n <h3>Velocity in a Plane<\/h3>\n <p>\n Velocity is the rate of change of position. In two dimensions, each component is treated independently:\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Velocity Components<\/div>\n <p>v = dr\/dt<\/p>\n <p>vx = dx\/dt [x-component of velocity]<\/p>\n <p>vy = dy\/dt [y-component of velocity]<\/p>\n <p>|v| = √(vx² + vy²)<\/p>\n <\/div>\n\n <p>\n The direction of velocity is always tangent to the path at that point. For a particle moving in a curved path, even if the speed (magnitude) remains constant, the direction of velocity changes \u2014 and that change in direction constitutes acceleration.\n <\/p>\n\n \n <a href=\"https:\/\/ksquareinstitute.in\/neet-2026-rank-predictor\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"display:block; margin-top:28px; margin-bottom:8px;\">\n <img decoding=\"async\" src=\"https:\/\/ksquareinstitute.in\/blog\/wp-content\/uploads\/2026\/03\/neet-2026-college-and-rank-predictor-scaled.png\"\n alt=\"NEET 2026 College and Rank Predictor - KSquare Career Institute\"\n style=\"width:100%; height:auto; border-radius:10px; display:block;\">\n <\/a>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">07<\/div>\n <h2 class=\"section-title\">Acceleration <span>in a Plane<\/span><\/h2>\n <\/div>\n\n <p>\n Acceleration is defined as the rate of change of velocity. In two dimensions it has both a component along the direction of motion (changing speed) and a component perpendicular to motion (changing direction).\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Acceleration Components<\/div>\n <p>a = dv\/dt<\/p>\n <p>ax = dvx\/dt [x-component of acceleration]<\/p>\n <p>ay = dvy\/dt [y-component of acceleration]<\/p>\n <p>|a| = √(ax² + ay²)<\/p>\n <\/div>\n\n <h3>Uniform vs Non-Uniform Acceleration<\/h3>\n <ul>\n <li><strong>Uniform acceleration:<\/strong> Both ax and ay are constant. The equations of motion for straight-line motion apply independently along each axis.<\/li>\n <li><strong>Non-uniform acceleration:<\/strong> At least one component varies with time. Requires calculus or graphical analysis.<\/li>\n <\/ul>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Key Insight for NEET<\/div>\n <p>In projectile motion, ax = 0 (no horizontal acceleration) and ay = −g (constant downward acceleration). This makes horizontal motion uniform and vertical motion uniformly accelerated \u2014 two independent 1D problems.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">08<\/div>\n <h2 class=\"section-title\">Relative Velocity in <span>Two Dimensions<\/span><\/h2>\n <\/div>\n\n <p>\n The velocity of an object as measured by an observer who is themselves in motion is called <strong>relative velocity<\/strong>. This concept is directly applied in river-boat problems and rain-wind problems that appear in NEET.\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Relative Velocity Formula<\/div>\n <p>vₐℬ = vₐ − vℬ<\/p>\n <p>[Velocity of A relative to B = velocity of A − velocity of B]<\/p>\n <\/div>\n\n <h3>River-Boat Problem (NEET Favorite)<\/h3>\n <p>\n A boat moves with velocity <strong>vₛ<\/strong> relative to water. The river flows with velocity <strong>vḐ<\/strong>. The resultant velocity of the boat relative to the ground is the vector sum of the two:\n <\/p>\n\n <div class=\"formula-orange\">\n <p>vḏḌṣṛ = vₛ + vḐ [vector addition]<\/p>\n <p>To reach directly opposite shore: vₛ must be directed upstream at angle θ = sin⁻¹(vḐ \/ vₛ)<\/p>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Warning<\/div>\n <p>Always specify: relative to what frame? The velocity of rain relative to a running person is different from the velocity of rain relative to the ground. Forgetting the reference frame is the most common error here.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">09<\/div>\n <h2 class=\"section-title\">Projectile Motion \u2014 <span>Complete Formula Sheet<\/span><\/h2>\n <\/div>\n\n <p>\n Projectile motion is the most heavily tested topic from <strong>Motion in a Plane Class 11 notes<\/strong> in NEET. A projectile is any object launched into the air with an initial velocity and then moving under gravity alone (no air resistance).\n <\/p>\n\n <h3>Component Breakdown<\/h3>\n <p>\n At time t = 0, a projectile is launched with speed u at angle θ above the horizontal. The motion splits into two independent components:\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Projectile Motion \u2014 Component Equations<\/div>\n <p>Horizontal (uniform motion, ax = 0):<\/p>\n <p> vx = u cosθ [constant throughout]<\/p>\n <p> x = u cosθ · t<\/p>\n <p><\/p>\n <p>Vertical (uniformly accelerated, ay = −g):<\/p>\n <p> vy = u sinθ − gt<\/p>\n <p> y = u sinθ · t − ½gt²<\/p>\n <\/div>\n\n <h3>Key Derived Results<\/h3>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Time of Flight, Maximum Height, Range<\/div>\n <p>T = (2u sinθ) \/ g [Total time of flight]<\/p>\n <p>H = (u² sin²θ) \/ (2g) [Maximum height]<\/p>\n <p>R = (u² sin2θ) \/ g [Horizontal range]<\/p>\n <p>R_max = u² \/ g (when θ = 45°)<\/p>\n <\/div>\n\n <h3>Equation of Trajectory<\/h3>\n <p>Eliminating t from the horizontal and vertical equations gives the path of the projectile:<\/p>\n\n <div class=\"formula-orange\">\n <p>y = x tanθ − (g x²) \/ (2u² cos²θ)<\/p>\n <p>This is a parabola \u2014 the standard trajectory of projectile motion.<\/p>\n <\/div>\n\n <h3>Complementary Angles<\/h3>\n <p>\n Two launch angles that add to 90° give the same horizontal range. For example, a projectile launched at 30° and another at 60° both travel the same horizontal distance (assuming the same initial speed on level ground).\n <\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Quantity<\/th>\n <th>Formula<\/th>\n <th>Maximized at θ =<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Range R<\/td>\n <td>u² sin2θ \/ g<\/td>\n <td>45°<\/td>\n <\/tr>\n <tr>\n <td>Height H<\/td>\n <td>u² sin²θ \/ 2g<\/td>\n <td>90°<\/td>\n <\/tr>\n <tr>\n <td>Time T<\/td>\n <td>2u sinθ \/ g<\/td>\n <td>90°<\/td>\n <\/tr>\n <tr>\n <td>Horizontal velocity<\/td>\n <td>u cosθ<\/td>\n <td>0° (horizontal launch)<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <a href=\"#\" rel=\"nofollow noopener noreferrer\" class=\"pdf-download-btn\">\n <svg width=\"18\" height=\"18\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M21 15v4a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2v-4\"\/><polyline points=\"7 10 12 15 17 10\"\/><line x1=\"12\" y1=\"15\" x2=\"12\" y2=\"3\"\/><\/svg>\n Download Full PDF Notes \u2014 Motion in a Plane Class 11\n <\/a>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">10<\/div>\n <h2 class=\"section-title\">Uniform Circular <span>Motion<\/span><\/h2>\n <\/div>\n\n <p>\n In uniform circular motion, an object moves along a circular path with <strong>constant speed<\/strong>. However, the direction of velocity changes continuously \u2014 meaning the object is <em>always accelerating<\/em>, even though its speed does not change.\n <\/p>\n\n <h3>Centripetal Acceleration<\/h3>\n <p>\n The acceleration in uniform circular motion always points toward the center of the circle (centripetal = center-seeking). It arises purely from the change in direction, not change in speed.\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Uniform Circular Motion Formulas<\/div>\n <p>ac = v² \/ r [centripetal acceleration]<\/p>\n <p>ac = ω²r [in terms of angular velocity]<\/p>\n <p>T = 2πr \/ v = 2π \/ ω [time period]<\/p>\n <p>f = 1 \/ T [frequency]<\/p>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Critical Point for NEET<\/div>\n <p>The velocity vector is always tangential (perpendicular to the radius). The centripetal acceleration vector is always radially inward. These two are always perpendicular to each other in uniform circular motion.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">11<\/div>\n <h2 class=\"section-title\">Solved <span>Numerical Examples<\/span><\/h2>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 1 \u2014 <span>Resultant Vector<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> Two vectors A = 3i + 4j and B = 2i − j. Find the magnitude and direction of R = A + B.<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>Rx = 3 + 2 = 5; Ry = 4 + (−1) = 3<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>|R| = √(5² + 3²) = √(25 + 9) = √34 ≈ 5.83 units<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">3<\/div><p>θ = tan⁻¹(3\/5) = tan⁻¹(0.6) ≈ 30.96° with x-axis<\/p><\/div>\n <\/div>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 2 \u2014 <span>Projectile Motion<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> A ball is projected at u = 20 m\/s and θ = 30°. Find R, H, and T. (g = 10 m\/s²)<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>T = (2 × 20 × sin30°) \/ 10 = (2 × 20 × 0.5) \/ 10 = 2 s<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>H = (20² × sin²30°) \/ (2 × 10) = (400 × 0.25) \/ 20 = 5 m<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">3<\/div><p>R = (20² × sin60°) \/ 10 = (400 × 0.866) \/ 10 = 34.64 m<\/p><\/div>\n <\/div>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 3 \u2014 <span>Centripetal Acceleration<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> A car moves in a circle of radius 50 m at a speed of 10 m\/s. Find the centripetal acceleration.<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>ac = v² \/ r = (10)² \/ 50 = 100 \/ 50 = 2 m\/s²<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>Direction: toward the center of the circular path<\/p><\/div>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">12<\/div>\n <h2 class=\"section-title\">Practice <span>Questions<\/span><\/h2>\n <\/div>\n\n <h3>Conceptual Questions<\/h3>\n <ol>\n <li>Can a vector have zero magnitude if one of its components is non-zero? Justify your answer.<\/li>\n <li>A ball is thrown horizontally from a cliff. Does it undergo projectile motion? Identify the horizontal and vertical components of motion.<\/li>\n <li>In uniform circular motion, why is the object said to be accelerating even though its speed is constant?<\/li>\n <li>Two projectiles are launched with the same initial speed but at 40° and 50°. Compare their ranges and heights.<\/li>\n <li>What is the direction of centripetal acceleration? Can it ever be tangential?<\/li>\n <\/ol>\n\n <h3>Numerical Questions<\/h3>\n <ol>\n <li>Find the resultant of vectors P = 5i + 2j and Q = −3i + 4j. Determine its magnitude and angle with the x-axis.<\/li>\n <li>A projectile is fired with u = 40 m\/s at 45°. Calculate R, H, and T. (g = 10 m\/s²)<\/li>\n <li>A particle moves in a circle of radius 0.5 m with a period of 2 s. Find its speed, centripetal acceleration, and angular velocity.<\/li>\n <li>A boat can move at 5 m\/s in still water. A river flows at 3 m\/s. If the boat is aimed perpendicular to the bank, find its actual velocity and the angle of drift.<\/li>\n <\/ol>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">13<\/div>\n <h2 class=\"section-title\">PYQ <span>Trends \u2014 NEET Analysis<\/span><\/h2>\n <\/div>\n\n <p>\n Analysis of past 10 years of NEET papers shows that Motion in a Plane Class 11 notes contribute consistently 2\u20133 questions per paper. Below are the key high-yield topics observed in previous years:\n <\/p>\n\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2023<\/span> <strong>Projectile Motion:<\/strong> Finding horizontal range and time of flight for a given angle and initial speed. Direct formula application.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2022<\/span> <strong>Circular Motion:<\/strong> Centripetal acceleration calculation and relationship with angular velocity. Conceptual plus numerical.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2021<\/span> <strong>Relative Velocity:<\/strong> River-boat problem \u2014 finding minimum time and minimum drift conditions.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2020<\/span> <strong>Vector Addition:<\/strong> Resultant of two vectors at a given angle \u2014 both magnitude and direction.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2019<\/span> <strong>Projectile Trajectory:<\/strong> Equation of trajectory and identifying parabolic path parameters.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2018<\/span> <strong>Complementary Angles:<\/strong> Proving that angles θ and (90°−θ) give equal range for same initial speed.\n <\/div>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Exam Strategy<\/div>\n <p>Projectile motion questions in NEET are almost always direct formula applications. Memorize T, H, and R formulas with derivations. If you understand <em>why<\/em> the formulas work, you will never confuse sin vs sin² vs sin2θ.<\/p>\n <\/div>\n <\/div>\n\n <p style=\"margin-top:20px;\">\n For comprehensive NEET 2026 preparation material, explore:\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/31-umeed-neet-2026\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Umeed NEET 2026 Study Materials<\/a>,\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/29-pc4-29\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Grip NCERT Biology<\/a>, and\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/28-grip-ncert-chemistry\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Grip NCERT Chemistry<\/a>.\n <\/p>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">14<\/div>\n <h2 class=\"section-title\">Summary \u2014 <span>Quick Revision<\/span><\/h2>\n <\/div>\n\n <div class=\"revision-box\">\n <div class=\"rev-title\">✓ Motion in a Plane \u2014 Rapid Fire Revision Points<\/div>\n <ul>\n <li>Scalars have magnitude only; vectors have magnitude and direction<\/li>\n <li>Any 2D vector A = Ax i + Ay j; resolve before adding or subtracting<\/li>\n <li>Resultant magnitude: R = √(Rx² + Ry²); direction: θ = tan⁻¹(Ry\/Rx)<\/li>\n <li>Dot product A·B = AB cosθ (scalar); cross product |A×B| = AB sinθ (vector)<\/li>\n <li>Velocity: v = dr\/dt; acceleration: a = dv\/dt \u2014 both are vectors<\/li>\n <li>Relative velocity: vₐℬ = vₐ − vℬ<\/li>\n <li>Projectile: horizontal motion uniform (vx = u cosθ); vertical uniformly accelerated<\/li>\n <li>R = u²sin2θ\/g; H = u²sin²θ\/2g; T = 2u sinθ\/g<\/li>\n <li>Maximum range at θ = 45°; complementary angles give equal range<\/li>\n <li>UCM: speed constant, direction changes; centripetal acceleration = v²\/r (inward)<\/li>\n <li>Velocity is tangential; centripetal acceleration is radial \u2014 always perpendicular<\/li>\n <\/ul>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">15<\/div>\n <h2 class=\"section-title\">Common <span>Mistakes to Avoid<\/span><\/h2>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">1<\/div>\n <div class=\"mistake-content\">\n <strong>Adding vectors as scalars<\/strong>\n <p>Never add the magnitudes of two vectors directly unless they are parallel. Always resolve into components first, then add Rx and Ry separately.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">2<\/div>\n <div class=\"mistake-content\">\n <strong>Confusing sinθ, sin²θ, and sin2θ in projectile formulas<\/strong>\n <p>R uses sin2θ = 2sinθcosθ; H uses sin²θ; T uses sinθ. Writing the wrong term will give a completely wrong answer.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">3<\/div>\n <div class=\"mistake-content\">\n <strong>Ignoring sign convention in vertical motion<\/strong>\n <p>Always take upward as positive and downward as negative (or vice versa \u2014 but stay consistent). g must always oppose the initial vertical velocity for upward projectiles.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">4<\/div>\n <div class=\"mistake-content\">\n <strong>Thinking UCM means no acceleration<\/strong>\n <p>Constant speed does not mean zero acceleration. The direction of velocity is continuously changing \u2014 centripetal acceleration is always present and always points inward.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">5<\/div>\n <div class=\"mistake-content\">\n <strong>Omitting the reference frame in relative velocity problems<\/strong>\n <p>Always write vₐℬ clearly as “velocity of A with respect to B.” Mixing up vₐℬ and vℬₐ reverses your answer direction.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">6<\/div>\n <div class=\"mistake-content\">\n <strong>Using the wrong product type<\/strong>\n <p>Work = F·d (dot product, scalar result). Torque = r × F (cross product, vector result). Never mix these up in application problems.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">16<\/div>\n <h2 class=\"section-title\">Frequently Asked <span>Questions<\/span><\/h2>\n <\/div>\n\n <details class=\"faq-item\">\n <summary>\n What is the difference between distance and displacement in Motion in a Plane?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Distance is the total path length traveled (scalar \u2014 always positive). Displacement is the shortest straight-line vector from the initial to the final position. In a plane, displacement has both magnitude and direction. A particle can travel a large distance but have zero displacement if it returns to its starting point.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n Why does a projectile follow a parabolic path?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Because horizontal motion is uniform (constant velocity, x proportional to t) while vertical motion is uniformly accelerated (y proportional to t²). Substituting x = u cosθ · t into the vertical equation eliminates t and gives y as a quadratic function of x \u2014 the mathematical definition of a parabola.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n At what angle of projection is the horizontal range maximum?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>The horizontal range R = u² sin2θ \/ g. Since sin2θ is maximum when 2θ = 90°, the range is maximum at θ = 45°. At this angle, Rₖ₊ₓ = u² \/ g. For any other angle, the range is less than this maximum.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n How is centripetal acceleration different from tangential acceleration?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Centripetal acceleration (ac = v²\/r) is always directed toward the center of the circular path and is responsible for changing the direction of velocity. Tangential acceleration is directed along the velocity (tangent to the path) and is responsible for changing the speed. In uniform circular motion, tangential acceleration is zero; only centripetal acceleration exists.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n What is the significance of dot and cross products in NEET Physics?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>The dot product appears in Work (W = F·d = Fd cosθ) and Power calculations. The cross product appears in Torque (τ = r×F), Angular Momentum (L = r×p), and Magnetic Force (F = qv×B). NEET tests these primarily through application \u2014 recognizing which type of multiplication yields a scalar vs. a vector result.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n Can two vectors with unequal magnitudes produce a zero resultant?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>No. For the resultant of two vectors to be zero, they must be equal in magnitude and exactly opposite in direction (antiparallel). If their magnitudes differ, no direction can make them cancel completely \u2014 the resultant will always have a non-zero magnitude.<\/p>\n <\/div>\n <\/details>\n <\/div>\n\n\n \n <div class=\"cta-section\">\n <h2>Ready to Dominate NEET Physics?<\/h2>\n <p>Practice more problems, predict your rank, and access full course materials designed by top NEET educators at KSquare.<\/p>\n <div class=\"cta-buttons\">\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/3-mission-180-neet-physics-rankers-batch\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-white\">Join Mission 180 Physics Batch<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/neet-2026-rank-predictor\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-outline\">Use NEET 2026 Rank Predictor<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/free-study-material\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-outline\">Download Free Materials<\/a>\n <\/div>\n <\/div>\n\n<\/div>\n\n<\/body>\n<\/html>\n\n\n\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n <meta charset=\"UTF-8\">\n <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n <title>Table of Contents \u2014 Physics Class 11<\/title>\n \n \n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Plus+Jakarta+Sans:ital,wght@0,200..800;1,200..800&display=swap\" rel=\"stylesheet\">\n \n <style>\n \/* Scoped wrapper using a unique ID to prevent CSS conflicts. *\/\n #physics-toc-wrapper {\n font-family: 'DM Sans', sans-serif;\n width: 100%;\n margin: 0;\n padding: 60px 0;\n color: #111;\n background: #fff;\n -webkit-font-smoothing: antialiased;\n }\n\n #physics-toc-wrapper .container-inner {\n width: 100%;\n margin: 0 auto;\n padding: 0; \/* Set 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#physics-toc-wrapper tr:hover {\n background-color: #f8fafc;\n }\n\n #physics-toc-wrapper tr:last-child {\n border-bottom: none;\n }\n\n #physics-toc-wrapper td {\n padding: 24px 16px;\n vertical-align: middle;\n font-size: 1.05rem;\n font-weight: 500;\n border-right: 1px solid #e4e4e7;\n }\n\n #physics-toc-wrapper td:last-child {\n border-right: none;\n }\n\n \/* First column (Numbers) alignment and padding *\/\n #physics-toc-wrapper td:first-child {\n color: #a1a1aa;\n font-size: 0.9rem;\n width: 70px;\n font-weight: 400;\n font-variant-numeric: tabular-nums;\n text-align: center;\n padding-left: 10px;\n }\n\n \/* Middle column (Chapter Name) alignment and padding *\/\n #physics-toc-wrapper td:nth-child(2) {\n padding-left: 24px;\n color: #18181b;\n }\n\n \/* Last column (Button) alignment and padding *\/\n #physics-toc-wrapper td:last-child {\n text-align: right;\n width: 180px;\n padding-right: 16px;\n }\n\n \/* Button Styling *\/\n #physics-toc-wrapper a.go {\n display: inline-block;\n font-family: 'Plus Jakarta Sans', sans-serif;\n font-size: 0.75rem;\n font-weight: 800;\n padding: 12px 24px;\n border: 1.5px solid #18181b;\n border-radius: 8px;\n color: #18181b;\n text-decoration: none;\n letter-spacing: 0.05em;\n text-transform: uppercase;\n transition: all 0.2s cubic-bezier(0.4, 0, 0.2, 1);\n white-space: nowrap;\n }\n\n #physics-toc-wrapper a.go:hover {\n background: #18181b;\n color: #ffffff;\n transform: translateY(-2px);\n box-shadow: 0 4px 12px rgba(24, 24, 27, 0.15);\n }\n\n \/* Responsive adjustments *\/\n @media (max-width: 768px) {\n #physics-toc-wrapper h2 {\n font-size: 1.75rem;\n margin-bottom: 32px;\n }\n #physics-toc-wrapper td {\n padding: 18px 12px;\n font-size: 0.95rem;\n }\n }\n <\/style>\n<\/head>\n<body>\n\n<div id=\"physics-toc-wrapper\">\n <div class=\"container-inner\">\n <h1>Table of Contents<\/h1>\n <h2>Physics — Class 11<\/h2>\n \n <table>\n <tr><td>01<\/td><td>Units and Measurements<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/units-and-measurements-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>02<\/td><td>Motion in a Straight Line<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/motion-in-a-straight-line-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>03<\/td><td>Motion in a Plane<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/motion-in-a-plane-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>04<\/td><td>Laws of Motion<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/laws-of-motion-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>05<\/td><td>Work, Energy and Power<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/work-energy-and-power-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>06<\/td><td>System of Particles and Rotational Motion<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/system-of-particles-and-rotational-motion-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>07<\/td><td>Gravitation<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/gravitation-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>08<\/td><td>Mechanical Properties of Solids<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/mechanical-properties-of-solids-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>09<\/td><td>Mechanical Properties of Fluids<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/mechanical-properties-of-fluids-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>10<\/td><td>Thermal Properties of Matter<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/thermal-properties-of-matter-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>11<\/td><td>Thermodynamics<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/thermodynamics-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>12<\/td><td>Kinetic Theory<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/kinetic-theory-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>13<\/td><td>Oscillations<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/oscillations-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>14<\/td><td>Waves<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/waves-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <\/table>\n <\/div>\n<\/div>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Motion in a Plane Class 11 Notes | NEET Physics | KSquare 01 Introduction to Motion in a Plane Mastering Motion in a Plane Class 11 notes is essential for every NEET aspirant targeting a top score in Physics. In Class 11 Chapter 4, motion is extended from a single straight line into a two-dimensional […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[127],"tags":[],"class_list":["post-3925","post","type-post","status-publish","format-standard","hentry","category-free-study-material"],"blocksy_meta":{"page_structure_type":"type-1","styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":6}},"_links":{"self":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/comments?post=3925"}],"version-history":[{"count":7,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925\/revisions"}],"predecessor-version":[{"id":4206,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925\/revisions\/4206"}],"wp:attachment":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/media?parent=3925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/categories?post=3925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/tags?post=3925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":3925,"date":"2026-03-26T12:47:59","date_gmt":"2026-03-26T12:47:59","guid":{"rendered":"https:\/\/ksquareinstitute.in\/blog\/?p=3925"},"modified":"2026-04-03T12:08:30","modified_gmt":"2026-04-03T12:08:30","slug":"motion-in-a-plane-class-11-notes","status":"publish","type":"post","link":"https:\/\/ksquareinstitute.in\/blog\/motion-in-a-plane-class-11-notes\/","title":{"rendered":"Motion in a Plane Class 11 Notes | Vectors, Projectile Motion, Numericals & PYQs"},"content":{"rendered":"\n\n\n\n\n\nMotion in a Plane Class 11 Notes | NEET Physics | KSquare<\/title>\n<meta name=\"description\" content=\"Complete Motion in a Plane Class 11 Notes for NEET Physics. 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font-size: 14.5px; color: var(--muted); }\n\n \/* \u2500\u2500 PYQ TREND BADGE \u2500\u2500 *\/\n .pyq-year {\n display: inline-block;\n background: var(--dark);\n color: var(--accent);\n font-family: 'JetBrains Mono', monospace;\n font-size: 12px;\n font-weight: 600;\n padding: 3px 8px;\n border-radius: 4px;\n margin-right: 6px;\n }\n\n .pyq-item {\n padding: 14px 0;\n border-bottom: 1px solid var(--border);\n }\n\n .pyq-item:last-child { border-bottom: none; }\n\n \/* \u2500\u2500 RESPONSIVE \u2500\u2500 *\/\n @media (max-width: 768px) {\n .section { padding-top: 36px; padding-bottom: 36px; padding-left: 0; padding-right: 0; }\n .cta-section { padding: 44px 0; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"article-body\">\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">01<\/div>\n <h1 class=\"section-title\">Introduction to <span>Motion in a Plane<\/span><\/h1>\n <\/div>\n\n <p>\n Mastering <strong>Motion in a Plane Class 11 notes<\/strong> is essential for every NEET aspirant targeting a top score in Physics. In Class 11 Chapter 4, motion is extended from a single straight line into a two-dimensional coordinate plane \u2014 and this shift demands a completely new set of mathematical tools: <strong>vectors<\/strong>.\n <\/p>\n <p>\n When an object moves along a straight line, a single number with a sign (+\/\u2212) describes its state completely. The moment motion occurs along a curved path \u2014 a ball thrown into the air, a boat crossing a river, a satellite orbiting Earth \u2014 a single scalar number is no longer sufficient. You need both <em>magnitude<\/em> and <em>direction<\/em>, which is exactly what vectors provide.\n <\/p>\n <p>\n This chapter lays the mathematical and conceptual foundation for two of the most important topics in NEET Physics: <strong>projectile motion<\/strong> and <strong>uniform circular motion<\/strong>. Every derivation, every formula, and every numerical problem in this chapter traces back to one core skill \u2014 resolving a vector into its perpendicular components along the x and y axes.\n <\/p>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Why This Chapter Matters for NEET<\/div>\n <p>Motion in a Plane consistently appears in NEET with 2\u20133 direct questions. Projectile motion alone accounts for roughly 1\u20132 questions per year. Strong conceptual clarity here also supports Laws of Motion and Work-Energy chapters.<\/p>\n <\/div>\n <\/div>\n\n <h3>Related Reading<\/h3>\n <div class=\"related-links\">\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/neet-physics-survival-kit-2026\/\" class=\"related-link\">NEET Physics Survival Kit 2026<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/organic-chemistry-strategy-neet\/\" class=\"related-link\">Organic Chemistry Strategy NEET<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/neet-biology-tricks-for-exams\/\" class=\"related-link\">NEET Biology Tricks for Exams<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/score-340-in-neet-biology\/\" class=\"related-link\">How to Score 340+ in NEET Biology<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/blog\/top-10-tricky-neet-biology-diagrams\/\" class=\"related-link\">Top 10 Tricky NEET Biology Diagrams<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/free-study-material\/\" class=\"related-link\">Free Study Materials \u2014 KSquare<\/a>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">02<\/div>\n <h2 class=\"section-title\">Scalars and <span>Vectors<\/span><\/h2>\n <\/div>\n\n <p>\n The most fundamental distinction in mechanics is between <strong>scalar<\/strong> and <strong>vector<\/strong> quantities.\n <\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Feature<\/th>\n <th>Scalar<\/th>\n <th>Vector<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Definition<\/td>\n <td>Magnitude only<\/td>\n <td>Magnitude + Direction<\/td>\n <\/tr>\n <tr>\n <td>Examples<\/td>\n <td>Mass, Temperature, Distance, Speed, Energy<\/td>\n <td>Displacement, Velocity, Acceleration, Force<\/td>\n <\/tr>\n <tr>\n <td>Notation<\/td>\n <td>Plain symbol: m, T<\/td>\n <td>Bold or arrow: <strong>A<\/strong>, ⃗A<\/td>\n <\/tr>\n <tr>\n <td>Addition rule<\/td>\n <td>Ordinary algebra<\/td>\n <td>Vector (triangle\/parallelogram) law<\/td>\n <\/tr>\n <tr>\n <td>Negative value<\/td>\n <td>Means smaller\/zero<\/td>\n <td>Means opposite direction<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Warning \u2014 Common Confusion<\/div>\n <p>Speed is scalar; velocity is vector. Distance is scalar; displacement is vector. NEET frequently tests this distinction \u2014 never use them interchangeably.<\/p>\n <\/div>\n <\/div>\n\n \n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/3-mission-180-neet-physics-rankers-batch\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"display:block; margin-top:28px; margin-bottom:8px;\">\n <img decoding=\"async\" src=\"https:\/\/ksquareinstitute.in\/blog\/wp-content\/uploads\/2026\/03\/Course-Poromo-Banner-scaled.png\"\n alt=\"Mission 180 NEET Physics Rankers Batch - KSquare Career Institute\"\n style=\"width:100%; height:auto; border-radius:10px; display:block;\">\n <\/a>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">03<\/div>\n <h2 class=\"section-title\">Vector Representation \u2014 <span>Components & Unit Vectors<\/span><\/h2>\n <\/div>\n\n <p>\n Any vector in a 2D plane can be completely expressed using its <strong>rectangular components<\/strong> along the x-axis and y-axis. This is the most powerful technique in Motion in a Plane Class 11 notes and is used throughout the chapter.\n <\/p>\n\n <h3>Unit Vectors<\/h3>\n <p>\n A unit vector has magnitude exactly equal to 1 and points along a specified direction. The standard unit vectors in 2D are:\n <\/p>\n <ul>\n <li><strong>î<\/strong> \u2014 unit vector along the positive x-axis<\/li>\n <li><strong>ĵ<\/strong> \u2014 unit vector along the positive y-axis<\/li>\n <li><strong>k̂<\/strong> \u2014 unit vector along the positive z-axis (for 3D)<\/li>\n <\/ul>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Vector in Component Form<\/div>\n <p>A = Ax i + Ay j<\/p>\n <p>|A| = √(Ax² + Ay²)<\/p>\n <p>θ = tan⁻¹(Ay \/ Ax) [angle with x-axis]<\/p>\n <\/div>\n\n <p>\n The components Ax = |A| cosθ and Ay = |A| sinθ allow you to separate any 2D problem into two independent 1D problems \u2014 one along x, one along y.\n <\/p>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Tip \u2014 Resolution Strategy<\/div>\n <p>Always choose axes such that maximum vectors lie along one axis. This minimizes the number of components you need to calculate and reduces arithmetic errors.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">04<\/div>\n <h2 class=\"section-title\">Vector Addition and <span>Subtraction<\/span><\/h2>\n <\/div>\n\n <h3>Graphical Methods<\/h3>\n <p>\n <strong>Triangle Law:<\/strong> Place the tail of the second vector at the head of the first. The resultant is drawn from the tail of the first to the head of the second vector.<br>\n <strong>Parallelogram Law:<\/strong> Place both vectors tail-to-tail. The diagonal of the parallelogram formed represents the resultant.\n <\/p>\n\n <h3>Analytical Method (Component Addition)<\/h3>\n <p>This is the method used in all numerical problems. Add corresponding components separately:<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Resultant of Two Vectors A1 and A2<\/div>\n <p>Rx = A1x + A2x<\/p>\n <p>Ry = A1y + A2y<\/p>\n <p>R = √(Rx² + Ry²)<\/p>\n <p>tanθ = Ry \/ Rx<\/p>\n <\/div>\n\n <h3>Vector Subtraction<\/h3>\n <p>\n Subtraction is defined as adding the negative vector. Reversing a vector reverses its direction but keeps the same magnitude:\n <\/p>\n\n <div class=\"formula-orange\">\n <p>A − B = A + (−B)<\/p>\n <p>−B has the same magnitude as B but points in the opposite direction<\/p>\n <\/div>\n\n <p>\n Both graphical and component methods apply. In component form: Rx = Ax − Bx and Ry = Ay − By.\n <\/p>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">05<\/div>\n <h2 class=\"section-title\">Multiplication of Vectors \u2014 <span>Dot & Cross Product<\/span><\/h2>\n <\/div>\n\n <p>\n Two types of vector multiplication appear in Class 11 Physics. Understanding when to use each is critical for NEET.\n <\/p>\n\n <h3>Scalar (Dot) Product<\/h3>\n <p>Produces a scalar result. Measures the projection of one vector along another.<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Dot Product<\/div>\n <p>A \u00b7 B = AB cosθ<\/p>\n <p>W = F \u00b7 d = Fd cosθ [Work is a dot product]<\/p>\n <p>If θ = 90° → A \u00b7 B = 0 (perpendicular vectors)<\/p>\n <p>If θ = 0° → A \u00b7 B = AB (parallel vectors)<\/p>\n <\/div>\n\n <h3>Vector (Cross) Product<\/h3>\n <p>Produces a vector result. The resultant is perpendicular to both original vectors.<\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Cross Product<\/div>\n <p>|A × B| = AB sinθ<\/p>\n <p>τ = r × F [Torque is a cross product]<\/p>\n <p>If θ = 0° → |A × B| = 0 (parallel vectors)<\/p>\n <p>If θ = 90° → |A × B| = AB (maximum)<\/p>\n <\/div>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Property<\/th>\n <th>Dot Product<\/th>\n <th>Cross Product<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Result type<\/td>\n <td>Scalar<\/td>\n <td>Vector<\/td>\n <\/tr>\n <tr>\n <td>Formula<\/td>\n <td>AB cosθ<\/td>\n <td>AB sinθ<\/td>\n <\/tr>\n <tr>\n <td>Commutative?<\/td>\n <td>Yes: A\u00b7B = B\u00b7A<\/td>\n <td>No: A×B = −(B×A)<\/td>\n <\/tr>\n <tr>\n <td>Application<\/td>\n <td>Work, Power<\/td>\n <td>Torque, Angular momentum<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">06<\/div>\n <h2 class=\"section-title\">Position, Displacement, and <span>Velocity in a Plane<\/span><\/h2>\n <\/div>\n\n <p>\n The concepts of position, displacement, and velocity are extended into two dimensions by expressing them as vectors using the component form learned earlier.\n <\/p>\n\n <h3>Position Vector<\/h3>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Position & Displacement<\/div>\n <p>r = x i + y j [position vector]<\/p>\n <p>Δr = r₂ − r₁ = (x₂−x₁) i + (y₂−y₁) j [displacement]<\/p>\n <\/div>\n\n <h3>Velocity in a Plane<\/h3>\n <p>\n Velocity is the rate of change of position. In two dimensions, each component is treated independently:\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Velocity Components<\/div>\n <p>v = dr\/dt<\/p>\n <p>vx = dx\/dt [x-component of velocity]<\/p>\n <p>vy = dy\/dt [y-component of velocity]<\/p>\n <p>|v| = √(vx² + vy²)<\/p>\n <\/div>\n\n <p>\n The direction of velocity is always tangent to the path at that point. For a particle moving in a curved path, even if the speed (magnitude) remains constant, the direction of velocity changes \u2014 and that change in direction constitutes acceleration.\n <\/p>\n\n \n <a href=\"https:\/\/ksquareinstitute.in\/neet-2026-rank-predictor\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"display:block; margin-top:28px; margin-bottom:8px;\">\n <img decoding=\"async\" src=\"https:\/\/ksquareinstitute.in\/blog\/wp-content\/uploads\/2026\/03\/neet-2026-college-and-rank-predictor-scaled.png\"\n alt=\"NEET 2026 College and Rank Predictor - KSquare Career Institute\"\n style=\"width:100%; height:auto; border-radius:10px; display:block;\">\n <\/a>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">07<\/div>\n <h2 class=\"section-title\">Acceleration <span>in a Plane<\/span><\/h2>\n <\/div>\n\n <p>\n Acceleration is defined as the rate of change of velocity. In two dimensions it has both a component along the direction of motion (changing speed) and a component perpendicular to motion (changing direction).\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Acceleration Components<\/div>\n <p>a = dv\/dt<\/p>\n <p>ax = dvx\/dt [x-component of acceleration]<\/p>\n <p>ay = dvy\/dt [y-component of acceleration]<\/p>\n <p>|a| = √(ax² + ay²)<\/p>\n <\/div>\n\n <h3>Uniform vs Non-Uniform Acceleration<\/h3>\n <ul>\n <li><strong>Uniform acceleration:<\/strong> Both ax and ay are constant. The equations of motion for straight-line motion apply independently along each axis.<\/li>\n <li><strong>Non-uniform acceleration:<\/strong> At least one component varies with time. Requires calculus or graphical analysis.<\/li>\n <\/ul>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Key Insight for NEET<\/div>\n <p>In projectile motion, ax = 0 (no horizontal acceleration) and ay = −g (constant downward acceleration). This makes horizontal motion uniform and vertical motion uniformly accelerated \u2014 two independent 1D problems.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">08<\/div>\n <h2 class=\"section-title\">Relative Velocity in <span>Two Dimensions<\/span><\/h2>\n <\/div>\n\n <p>\n The velocity of an object as measured by an observer who is themselves in motion is called <strong>relative velocity<\/strong>. This concept is directly applied in river-boat problems and rain-wind problems that appear in NEET.\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Relative Velocity Formula<\/div>\n <p>vₐℬ = vₐ − vℬ<\/p>\n <p>[Velocity of A relative to B = velocity of A − velocity of B]<\/p>\n <\/div>\n\n <h3>River-Boat Problem (NEET Favorite)<\/h3>\n <p>\n A boat moves with velocity <strong>vₛ<\/strong> relative to water. The river flows with velocity <strong>vḐ<\/strong>. The resultant velocity of the boat relative to the ground is the vector sum of the two:\n <\/p>\n\n <div class=\"formula-orange\">\n <p>vḏḌṣṛ = vₛ + vḐ [vector addition]<\/p>\n <p>To reach directly opposite shore: vₛ must be directed upstream at angle θ = sin⁻¹(vḐ \/ vₛ)<\/p>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Warning<\/div>\n <p>Always specify: relative to what frame? The velocity of rain relative to a running person is different from the velocity of rain relative to the ground. Forgetting the reference frame is the most common error here.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">09<\/div>\n <h2 class=\"section-title\">Projectile Motion \u2014 <span>Complete Formula Sheet<\/span><\/h2>\n <\/div>\n\n <p>\n Projectile motion is the most heavily tested topic from <strong>Motion in a Plane Class 11 notes<\/strong> in NEET. A projectile is any object launched into the air with an initial velocity and then moving under gravity alone (no air resistance).\n <\/p>\n\n <h3>Component Breakdown<\/h3>\n <p>\n At time t = 0, a projectile is launched with speed u at angle θ above the horizontal. The motion splits into two independent components:\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Projectile Motion \u2014 Component Equations<\/div>\n <p>Horizontal (uniform motion, ax = 0):<\/p>\n <p> vx = u cosθ [constant throughout]<\/p>\n <p> x = u cosθ · t<\/p>\n <p><\/p>\n <p>Vertical (uniformly accelerated, ay = −g):<\/p>\n <p> vy = u sinθ − gt<\/p>\n <p> y = u sinθ · t − ½gt²<\/p>\n <\/div>\n\n <h3>Key Derived Results<\/h3>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Time of Flight, Maximum Height, Range<\/div>\n <p>T = (2u sinθ) \/ g [Total time of flight]<\/p>\n <p>H = (u² sin²θ) \/ (2g) [Maximum height]<\/p>\n <p>R = (u² sin2θ) \/ g [Horizontal range]<\/p>\n <p>R_max = u² \/ g (when θ = 45°)<\/p>\n <\/div>\n\n <h3>Equation of Trajectory<\/h3>\n <p>Eliminating t from the horizontal and vertical equations gives the path of the projectile:<\/p>\n\n <div class=\"formula-orange\">\n <p>y = x tanθ − (g x²) \/ (2u² cos²θ)<\/p>\n <p>This is a parabola \u2014 the standard trajectory of projectile motion.<\/p>\n <\/div>\n\n <h3>Complementary Angles<\/h3>\n <p>\n Two launch angles that add to 90° give the same horizontal range. For example, a projectile launched at 30° and another at 60° both travel the same horizontal distance (assuming the same initial speed on level ground).\n <\/p>\n\n <div class=\"table-wrap\">\n <table>\n <thead>\n <tr>\n <th>Quantity<\/th>\n <th>Formula<\/th>\n <th>Maximized at θ =<\/th>\n <\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td>Range R<\/td>\n <td>u² sin2θ \/ g<\/td>\n <td>45°<\/td>\n <\/tr>\n <tr>\n <td>Height H<\/td>\n <td>u² sin²θ \/ 2g<\/td>\n <td>90°<\/td>\n <\/tr>\n <tr>\n <td>Time T<\/td>\n <td>2u sinθ \/ g<\/td>\n <td>90°<\/td>\n <\/tr>\n <tr>\n <td>Horizontal velocity<\/td>\n <td>u cosθ<\/td>\n <td>0° (horizontal launch)<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <a href=\"#\" rel=\"nofollow noopener noreferrer\" class=\"pdf-download-btn\">\n <svg width=\"18\" height=\"18\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M21 15v4a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2v-4\"\/><polyline points=\"7 10 12 15 17 10\"\/><line x1=\"12\" y1=\"15\" x2=\"12\" y2=\"3\"\/><\/svg>\n Download Full PDF Notes \u2014 Motion in a Plane Class 11\n <\/a>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">10<\/div>\n <h2 class=\"section-title\">Uniform Circular <span>Motion<\/span><\/h2>\n <\/div>\n\n <p>\n In uniform circular motion, an object moves along a circular path with <strong>constant speed<\/strong>. However, the direction of velocity changes continuously \u2014 meaning the object is <em>always accelerating<\/em>, even though its speed does not change.\n <\/p>\n\n <h3>Centripetal Acceleration<\/h3>\n <p>\n The acceleration in uniform circular motion always points toward the center of the circle (centripetal = center-seeking). It arises purely from the change in direction, not change in speed.\n <\/p>\n\n <div class=\"formula-dark\">\n <div class=\"formula-label\">Uniform Circular Motion Formulas<\/div>\n <p>ac = v² \/ r [centripetal acceleration]<\/p>\n <p>ac = ω²r [in terms of angular velocity]<\/p>\n <p>T = 2πr \/ v = 2π \/ ω [time period]<\/p>\n <p>f = 1 \/ T [frequency]<\/p>\n <\/div>\n\n <div class=\"callout callout-warning\">\n <div class=\"callout-icon\">⚠<\/div>\n <div>\n <div class=\"callout-title\">Critical Point for NEET<\/div>\n <p>The velocity vector is always tangential (perpendicular to the radius). The centripetal acceleration vector is always radially inward. These two are always perpendicular to each other in uniform circular motion.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">11<\/div>\n <h2 class=\"section-title\">Solved <span>Numerical Examples<\/span><\/h2>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 1 \u2014 <span>Resultant Vector<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> Two vectors A = 3i + 4j and B = 2i − j. Find the magnitude and direction of R = A + B.<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>Rx = 3 + 2 = 5; Ry = 4 + (−1) = 3<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>|R| = √(5² + 3²) = √(25 + 9) = √34 ≈ 5.83 units<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">3<\/div><p>θ = tan⁻¹(3\/5) = tan⁻¹(0.6) ≈ 30.96° with x-axis<\/p><\/div>\n <\/div>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 2 \u2014 <span>Projectile Motion<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> A ball is projected at u = 20 m\/s and θ = 30°. Find R, H, and T. (g = 10 m\/s²)<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>T = (2 × 20 × sin30°) \/ 10 = (2 × 20 × 0.5) \/ 10 = 2 s<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>H = (20² × sin²30°) \/ (2 × 10) = (400 × 0.25) \/ 20 = 5 m<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">3<\/div><p>R = (20² × sin60°) \/ 10 = (400 × 0.866) \/ 10 = 34.64 m<\/p><\/div>\n <\/div>\n <\/div>\n\n <div class=\"example-card\">\n <div class=\"example-head\">Example 3 \u2014 <span>Centripetal Acceleration<\/span><\/div>\n <div class=\"example-body\">\n <p><strong>Problem:<\/strong> A car moves in a circle of radius 50 m at a speed of 10 m\/s. Find the centripetal acceleration.<\/p>\n <div class=\"example-step\"><div class=\"example-step-num\">1<\/div><p>ac = v² \/ r = (10)² \/ 50 = 100 \/ 50 = 2 m\/s²<\/p><\/div>\n <div class=\"example-step\"><div class=\"example-step-num\">2<\/div><p>Direction: toward the center of the circular path<\/p><\/div>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">12<\/div>\n <h2 class=\"section-title\">Practice <span>Questions<\/span><\/h2>\n <\/div>\n\n <h3>Conceptual Questions<\/h3>\n <ol>\n <li>Can a vector have zero magnitude if one of its components is non-zero? Justify your answer.<\/li>\n <li>A ball is thrown horizontally from a cliff. Does it undergo projectile motion? Identify the horizontal and vertical components of motion.<\/li>\n <li>In uniform circular motion, why is the object said to be accelerating even though its speed is constant?<\/li>\n <li>Two projectiles are launched with the same initial speed but at 40° and 50°. Compare their ranges and heights.<\/li>\n <li>What is the direction of centripetal acceleration? Can it ever be tangential?<\/li>\n <\/ol>\n\n <h3>Numerical Questions<\/h3>\n <ol>\n <li>Find the resultant of vectors P = 5i + 2j and Q = −3i + 4j. Determine its magnitude and angle with the x-axis.<\/li>\n <li>A projectile is fired with u = 40 m\/s at 45°. Calculate R, H, and T. (g = 10 m\/s²)<\/li>\n <li>A particle moves in a circle of radius 0.5 m with a period of 2 s. Find its speed, centripetal acceleration, and angular velocity.<\/li>\n <li>A boat can move at 5 m\/s in still water. A river flows at 3 m\/s. If the boat is aimed perpendicular to the bank, find its actual velocity and the angle of drift.<\/li>\n <\/ol>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">13<\/div>\n <h2 class=\"section-title\">PYQ <span>Trends \u2014 NEET Analysis<\/span><\/h2>\n <\/div>\n\n <p>\n Analysis of past 10 years of NEET papers shows that Motion in a Plane Class 11 notes contribute consistently 2\u20133 questions per paper. Below are the key high-yield topics observed in previous years:\n <\/p>\n\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2023<\/span> <strong>Projectile Motion:<\/strong> Finding horizontal range and time of flight for a given angle and initial speed. Direct formula application.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2022<\/span> <strong>Circular Motion:<\/strong> Centripetal acceleration calculation and relationship with angular velocity. Conceptual plus numerical.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2021<\/span> <strong>Relative Velocity:<\/strong> River-boat problem \u2014 finding minimum time and minimum drift conditions.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2020<\/span> <strong>Vector Addition:<\/strong> Resultant of two vectors at a given angle \u2014 both magnitude and direction.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2019<\/span> <strong>Projectile Trajectory:<\/strong> Equation of trajectory and identifying parabolic path parameters.\n <\/div>\n <div class=\"pyq-item\">\n <span class=\"pyq-year\">2018<\/span> <strong>Complementary Angles:<\/strong> Proving that angles θ and (90°−θ) give equal range for same initial speed.\n <\/div>\n\n <div class=\"callout callout-tip\">\n <div class=\"callout-icon\">ⓘ<\/div>\n <div>\n <div class=\"callout-title\">Exam Strategy<\/div>\n <p>Projectile motion questions in NEET are almost always direct formula applications. Memorize T, H, and R formulas with derivations. If you understand <em>why<\/em> the formulas work, you will never confuse sin vs sin² vs sin2θ.<\/p>\n <\/div>\n <\/div>\n\n <p style=\"margin-top:20px;\">\n For comprehensive NEET 2026 preparation material, explore:\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/31-umeed-neet-2026\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Umeed NEET 2026 Study Materials<\/a>,\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/29-pc4-29\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Grip NCERT Biology<\/a>, and\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/28-grip-ncert-chemistry\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" style=\"color:var(--accent); font-weight:600;\">Grip NCERT Chemistry<\/a>.\n <\/p>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">14<\/div>\n <h2 class=\"section-title\">Summary \u2014 <span>Quick Revision<\/span><\/h2>\n <\/div>\n\n <div class=\"revision-box\">\n <div class=\"rev-title\">✓ Motion in a Plane \u2014 Rapid Fire Revision Points<\/div>\n <ul>\n <li>Scalars have magnitude only; vectors have magnitude and direction<\/li>\n <li>Any 2D vector A = Ax i + Ay j; resolve before adding or subtracting<\/li>\n <li>Resultant magnitude: R = √(Rx² + Ry²); direction: θ = tan⁻¹(Ry\/Rx)<\/li>\n <li>Dot product A·B = AB cosθ (scalar); cross product |A×B| = AB sinθ (vector)<\/li>\n <li>Velocity: v = dr\/dt; acceleration: a = dv\/dt \u2014 both are vectors<\/li>\n <li>Relative velocity: vₐℬ = vₐ − vℬ<\/li>\n <li>Projectile: horizontal motion uniform (vx = u cosθ); vertical uniformly accelerated<\/li>\n <li>R = u²sin2θ\/g; H = u²sin²θ\/2g; T = 2u sinθ\/g<\/li>\n <li>Maximum range at θ = 45°; complementary angles give equal range<\/li>\n <li>UCM: speed constant, direction changes; centripetal acceleration = v²\/r (inward)<\/li>\n <li>Velocity is tangential; centripetal acceleration is radial \u2014 always perpendicular<\/li>\n <\/ul>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section\">\n <div class=\"section-header\">\n <div class=\"badge\">15<\/div>\n <h2 class=\"section-title\">Common <span>Mistakes to Avoid<\/span><\/h2>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">1<\/div>\n <div class=\"mistake-content\">\n <strong>Adding vectors as scalars<\/strong>\n <p>Never add the magnitudes of two vectors directly unless they are parallel. Always resolve into components first, then add Rx and Ry separately.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">2<\/div>\n <div class=\"mistake-content\">\n <strong>Confusing sinθ, sin²θ, and sin2θ in projectile formulas<\/strong>\n <p>R uses sin2θ = 2sinθcosθ; H uses sin²θ; T uses sinθ. Writing the wrong term will give a completely wrong answer.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">3<\/div>\n <div class=\"mistake-content\">\n <strong>Ignoring sign convention in vertical motion<\/strong>\n <p>Always take upward as positive and downward as negative (or vice versa \u2014 but stay consistent). g must always oppose the initial vertical velocity for upward projectiles.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">4<\/div>\n <div class=\"mistake-content\">\n <strong>Thinking UCM means no acceleration<\/strong>\n <p>Constant speed does not mean zero acceleration. The direction of velocity is continuously changing \u2014 centripetal acceleration is always present and always points inward.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">5<\/div>\n <div class=\"mistake-content\">\n <strong>Omitting the reference frame in relative velocity problems<\/strong>\n <p>Always write vₐℬ clearly as “velocity of A with respect to B.” Mixing up vₐℬ and vℬₐ reverses your answer direction.<\/p>\n <\/div>\n <\/div>\n\n <div class=\"mistake-item\">\n <div class=\"mistake-num\">6<\/div>\n <div class=\"mistake-content\">\n <strong>Using the wrong product type<\/strong>\n <p>Work = F·d (dot product, scalar result). Torque = r × F (cross product, vector result). Never mix these up in application problems.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n\n \n <div class=\"section section-alt\">\n <div class=\"section-header\">\n <div class=\"badge\">16<\/div>\n <h2 class=\"section-title\">Frequently Asked <span>Questions<\/span><\/h2>\n <\/div>\n\n <details class=\"faq-item\">\n <summary>\n What is the difference between distance and displacement in Motion in a Plane?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Distance is the total path length traveled (scalar \u2014 always positive). Displacement is the shortest straight-line vector from the initial to the final position. In a plane, displacement has both magnitude and direction. A particle can travel a large distance but have zero displacement if it returns to its starting point.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n Why does a projectile follow a parabolic path?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Because horizontal motion is uniform (constant velocity, x proportional to t) while vertical motion is uniformly accelerated (y proportional to t²). Substituting x = u cosθ · t into the vertical equation eliminates t and gives y as a quadratic function of x \u2014 the mathematical definition of a parabola.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n At what angle of projection is the horizontal range maximum?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>The horizontal range R = u² sin2θ \/ g. Since sin2θ is maximum when 2θ = 90°, the range is maximum at θ = 45°. At this angle, Rₖ₊ₓ = u² \/ g. For any other angle, the range is less than this maximum.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n How is centripetal acceleration different from tangential acceleration?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>Centripetal acceleration (ac = v²\/r) is always directed toward the center of the circular path and is responsible for changing the direction of velocity. Tangential acceleration is directed along the velocity (tangent to the path) and is responsible for changing the speed. In uniform circular motion, tangential acceleration is zero; only centripetal acceleration exists.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n What is the significance of dot and cross products in NEET Physics?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>The dot product appears in Work (W = F·d = Fd cosθ) and Power calculations. The cross product appears in Torque (τ = r×F), Angular Momentum (L = r×p), and Magnetic Force (F = qv×B). NEET tests these primarily through application \u2014 recognizing which type of multiplication yields a scalar vs. a vector result.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"faq-item\">\n <summary>\n Can two vectors with unequal magnitudes produce a zero resultant?\n <span class=\"toggle\">+<\/span>\n <\/summary>\n <div class=\"faq-body\">\n <p>No. For the resultant of two vectors to be zero, they must be equal in magnitude and exactly opposite in direction (antiparallel). If their magnitudes differ, no direction can make them cancel completely \u2014 the resultant will always have a non-zero magnitude.<\/p>\n <\/div>\n <\/details>\n <\/div>\n\n\n \n <div class=\"cta-section\">\n <h2>Ready to Dominate NEET Physics?<\/h2>\n <p>Practice more problems, predict your rank, and access full course materials designed by top NEET educators at KSquare.<\/p>\n <div class=\"cta-buttons\">\n <a href=\"https:\/\/courses.ksquare.co.in\/new-courses\/3-mission-180-neet-physics-rankers-batch\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-white\">Join Mission 180 Physics Batch<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/neet-2026-rank-predictor\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-outline\">Use NEET 2026 Rank Predictor<\/a>\n <a href=\"https:\/\/ksquareinstitute.in\/free-study-material\/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"btn btn-outline\">Download Free Materials<\/a>\n <\/div>\n <\/div>\n\n<\/div>\n\n<\/body>\n<\/html>\n\n\n\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n <meta charset=\"UTF-8\">\n <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n <title>Table of Contents \u2014 Physics Class 11<\/title>\n \n \n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Plus+Jakarta+Sans:ital,wght@0,200..800;1,200..800&display=swap\" rel=\"stylesheet\">\n \n <style>\n \/* Scoped wrapper using a unique ID to prevent CSS conflicts. *\/\n #physics-toc-wrapper {\n font-family: 'DM Sans', sans-serif;\n width: 100%;\n margin: 0;\n padding: 60px 0;\n color: #111;\n background: #fff;\n -webkit-font-smoothing: antialiased;\n }\n\n #physics-toc-wrapper .container-inner {\n width: 100%;\n margin: 0 auto;\n padding: 0; \/* Set 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#physics-toc-wrapper tr:hover {\n background-color: #f8fafc;\n }\n\n #physics-toc-wrapper tr:last-child {\n border-bottom: none;\n }\n\n #physics-toc-wrapper td {\n padding: 24px 16px;\n vertical-align: middle;\n font-size: 1.05rem;\n font-weight: 500;\n border-right: 1px solid #e4e4e7;\n }\n\n #physics-toc-wrapper td:last-child {\n border-right: none;\n }\n\n \/* First column (Numbers) alignment and padding *\/\n #physics-toc-wrapper td:first-child {\n color: #a1a1aa;\n font-size: 0.9rem;\n width: 70px;\n font-weight: 400;\n font-variant-numeric: tabular-nums;\n text-align: center;\n padding-left: 10px;\n }\n\n \/* Middle column (Chapter Name) alignment and padding *\/\n #physics-toc-wrapper td:nth-child(2) {\n padding-left: 24px;\n color: #18181b;\n }\n\n \/* Last column (Button) alignment and padding *\/\n #physics-toc-wrapper td:last-child {\n text-align: right;\n width: 180px;\n padding-right: 16px;\n }\n\n \/* Button Styling *\/\n #physics-toc-wrapper a.go {\n display: inline-block;\n font-family: 'Plus Jakarta Sans', sans-serif;\n font-size: 0.75rem;\n font-weight: 800;\n padding: 12px 24px;\n border: 1.5px solid #18181b;\n border-radius: 8px;\n color: #18181b;\n text-decoration: none;\n letter-spacing: 0.05em;\n text-transform: uppercase;\n transition: all 0.2s cubic-bezier(0.4, 0, 0.2, 1);\n white-space: nowrap;\n }\n\n #physics-toc-wrapper a.go:hover {\n background: #18181b;\n color: #ffffff;\n transform: translateY(-2px);\n box-shadow: 0 4px 12px rgba(24, 24, 27, 0.15);\n }\n\n \/* Responsive adjustments *\/\n @media (max-width: 768px) {\n #physics-toc-wrapper h2 {\n font-size: 1.75rem;\n margin-bottom: 32px;\n }\n #physics-toc-wrapper td {\n padding: 18px 12px;\n font-size: 0.95rem;\n }\n }\n <\/style>\n<\/head>\n<body>\n\n<div id=\"physics-toc-wrapper\">\n <div class=\"container-inner\">\n <h1>Table of Contents<\/h1>\n <h2>Physics — Class 11<\/h2>\n \n <table>\n <tr><td>01<\/td><td>Units and Measurements<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/units-and-measurements-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>02<\/td><td>Motion in a Straight Line<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/motion-in-a-straight-line-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>03<\/td><td>Motion in a Plane<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/motion-in-a-plane-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>04<\/td><td>Laws of Motion<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/laws-of-motion-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>05<\/td><td>Work, Energy and Power<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/work-energy-and-power-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>06<\/td><td>System of Particles and Rotational Motion<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/system-of-particles-and-rotational-motion-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>07<\/td><td>Gravitation<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/gravitation-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>08<\/td><td>Mechanical Properties of Solids<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/mechanical-properties-of-solids-class-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>09<\/td><td>Mechanical Properties of Fluids<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/mechanical-properties-of-fluids-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>10<\/td><td>Thermal Properties of Matter<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/thermal-properties-of-matter-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>11<\/td><td>Thermodynamics<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/thermodynamics-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>12<\/td><td>Kinetic Theory<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/kinetic-theory-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>13<\/td><td>Oscillations<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/oscillations-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <tr><td>14<\/td><td>Waves<\/td><td><a class=\"go\" href=\"https:\/\/ksquareinstitute.in\/blog\/waves-11-notes\" target=\"_blank\">Go to page<\/a><\/td><\/tr>\n <\/table>\n <\/div>\n<\/div>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Motion in a Plane Class 11 Notes | NEET Physics | KSquare 01 Introduction to Motion in a Plane Mastering Motion in a Plane Class 11 notes is essential for every NEET aspirant targeting a top score in Physics. In Class 11 Chapter 4, motion is extended from a single straight line into a two-dimensional […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[127],"tags":[],"class_list":["post-3925","post","type-post","status-publish","format-standard","hentry","category-free-study-material"],"blocksy_meta":{"page_structure_type":"type-1","styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":6}},"_links":{"self":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/comments?post=3925"}],"version-history":[{"count":7,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925\/revisions"}],"predecessor-version":[{"id":4206,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/posts\/3925\/revisions\/4206"}],"wp:attachment":[{"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/media?parent=3925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/categories?post=3925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ksquareinstitute.in\/blog\/wp-json\/wp\/v2\/tags?post=3925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}