Chapter 3: Motion in a Plane
Motion in a Plane (kinematics in two dimensions) is where the straight-line grammar of Motion in a Straight Line grows a second axis — and where NTA quietly tests your vector discipline more than your calculus. This hub maps the complete chapter: scalars and vectors, graphical vector addition (triangle and parallelogram laws), resolution of vectors into rectangular components, analytical addition with the law of cosines, the scalar (dot) and vector (cross) products, motion in a plane with constant acceleration via independent x–y equations, relative velocity in two dimensions (river-boat and rain-umbrella problems), projectile motion with every derived formula, and uniform circular motion with centripetal acceleration a = v²/r. The exam pattern is predictable: component-splitting numericals, projectile range/height/flight-time questions, UCM integer answers on ω = v/r, and graph or diagram-interpretation MCQs. Work through the nine topic pages below in order, drill the practice questions on each, then sit the 30-question chapter test with its full answer key.
Topics in this chapter
- § 3.1 Scalars and Vectors — Class 11 Physics (NCERT 3.1–3.2, 3.3)Scalars and vectors Class 11 notes for JEE/NEET: definitions, position and displacement vectors, null and unit vectors, with solved examples and practice Qs.
- § 3.2 Vector Addition and Subtraction — Graphical Method (NCERT 3.3, 3.4)Triangle and parallelogram laws of vector addition: head-to-tail method, subtraction, maximum and minimum resultant, with solved examples and practice Qs for…
- § 3.3 Resolution of Vectors — Rectangular Components (NCERT 3.5)Resolution of vectors into rectangular components for JEE/NEET: A cos θ and A sin θ parts, unit vectors î ĵ k̂, quadrant care, examples and practice Qs.
- § 3.4 Vector Addition — Analytical Method (NCERT 3.6)Analytical vector addition for JEE/NEET: R = √(A²+B²+2AB cos θ) with derivation, direction formula tan α, special-angle cases, component method, practice Qs.
- § 3.5 Scalar and Vector Products — Dot & Cross (Syllabus Supplement)Dot and cross products for JEE/NEET: AB cos θ and AB sin θ, component rules, perpendicular and parallel tests, parallelogram area, examples and practice Qs.
- § 3.6 Motion in a Plane with Constant Acceleration (NCERT 3.7–3.8)Motion in a plane with constant acceleration for JEE/NEET: r(t) and v(t) in components, independent x and y equations, trajectory by eliminating t, practice…
- § 3.7 Relative Velocity in Two Dimensions — River-Boat & Rain (Syllabus Supplement)Relative velocity in two dimensions for JEE/NEET: v_AB = v_A − v_B, river-boat shortest time vs zero drift, rain-umbrella angle, examples and practice Qs.
- § 3.8 Projectile Motion — Trajectory, Time of Flight, Height, Range (NCERT 3.9)Projectile motion for Class 11 JEE/NEET: T, H, R and the trajectory equation derived step by step, horizontal projection, complementary angles, examples and…
- § 3.9 Uniform Circular Motion — Centripetal Acceleration a = v²/r (NCERT 3.10)Uniform circular motion for Class 11 JEE/NEET: why constant speed is accelerated motion, a = v²/r derivation, ω = v/r, period and rpm, examples and practice…
- ✓ Chapter testAttempt all questions, then submit to see your score and the explanation for every answer.