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Motion in a Plane

NCERT Class 11 Physics Chapter 3

Motion in a Plane for Class 11 Physics, JEE and NEET: scalars and vectors, vector addition and resolution, projectile motion and uniform circular motion.

9 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 3 “Motion in a Plane”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.2 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Scalars and vectors

    How scalar and vector quantities differ, why current is a scalar, displacement and equal vectors.

    NCERT Section 3.2 12 min read 6 solved examples 6 practice questions

  2. Multiplying a vector by a real number

    How the magnitude and direction change, the negative of a vector, parallel and unit vectors.

    NCERT Section 3.3 10 min read 5 solved examples 6 practice questions

  3. Adding and subtracting vectors graphically

    The triangle and parallelogram laws, the null vector and subtracting vectors, with solved examples.

    NCERT Section 3.4 13 min read 6 solved examples 6 practice questions

  4. Resolution of vectors

    Rectangular components A cos θ and A sin θ, unit vectors, magnitude, direction and direction cosines.

    NCERT Section 3.5 13 min read 6 solved examples 6 practice questions

  5. Adding vectors by components

    Adding vectors by components, magnitude and direction of the resultant, laws of cosines and sines.

    NCERT Section 3.6 13 min read 5 solved examples 6 practice questions

  6. Position, velocity and acceleration in a plane

    r = xî + yĵ, displacement, v = dr/dt along the tangent and a = dv/dt.

    NCERT Section 3.7 14 min read 5 solved examples 6 practice questions

  7. Motion in a plane with constant acceleration

    Vector equations of motion, x and y motions treated separately, with examples.

    NCERT Section 3.8 12 min read 5 solved examples 6 practice questions

  8. Projectile motion

    Formulas and derivations for time of flight, maximum height, horizontal range and the path, with examples.

    NCERT Section 3.9 15 min read 6 solved examples 7 practice questions

  9. Uniform circular motion

    Centripetal acceleration v/R, angular speed, time period and frequency, with solved examples.

    NCERT Section 3.10 13 min read 5 solved examples 6 practice questions

Key formulas in this chapter

Scalars and vectors

  • |A| = A (magnitude of vector A)
  • displacement = PP′ (initial position to final position)
  • |displacement| ≤ path length
  • A = B iff corresponding components are equal

Multiplying a vector by a number

  • |λA| = |λ| A
  • λ > 0: λA along A; λ < 0: λA opposite to A
  • 0A = 0 (null vector)
  • λ(A + B) = λA + λB
  • A = |A| n̂ (n̂ = unit vector along A)
  • displacement = constant velocity × elapsed time

Adding vectors graphically

  • R = A + B (tail of B at head of A)
  • A + B = B + A; (A + B) + C = A + (B + C)
  • A − B = A + (−B)
  • A + (−A) = 0; A + 0 = A
  • ||A| − |B|| ≤ |A + B| ≤ |A| + |B|

Resolution of vectors

  • A = λa + μb (resolution along two directions)
  • A = |A| n̂
  • A = Ax î + Ay ĵ
  • Ax = A cos θ; Ay = A sin θ
  • A = √(Ax^2 + Ay^2); tan θ = Ay/Ax
  • 3D: A = √(Ax^2 + Ay^2 + Az^2); cos2α + cos2β + cos2γ = 1

Adding vectors by components

  • Rx = Ax + Bx; Ry = Ay + By
  • R = √(Rx^2 + Ry^2); tan θ = Ry/Rx
  • R = √(A2 + B2 + 2AB cos θ)
  • tan α = B sin θ/(A + B cos θ)
  • R/sin θ = A/sin β = B/sin α
  • |A − B| = √(A2 + B2 − 2AB cos θ)

Position, velocity and acceleration in a plane

  • r = x î + y ĵ; Δr = r′ − r
  • v = dr/dt = vx î + vy ĵ; vx = dx/dt, vy = dy/dt
  • v = √(vx^2 + vy^2); tan θ = vy/vx
  • a = dv/dt = ax î + ay ĵ; ax = dvx/dt, ay = dvy/dt
  • rate of change of speed: dv/dt = (v·a)/|v|

Constant acceleration in a plane

  • v = v + at
  • r = r + vt + ½at
  • vx = v0x + ax t; vy = v0y + ay t
  • x = x0 + v0x t + ½ax t2; y = y0 + v0y t + ½ay t2
  • v = v + 2a·(r − r)

Projectile motion

  • x = (v cos θ) t; y = (v sin θ) t − ½gt
  • vx = v0 cos θ0; vy = v0 sin θ0 − gt
  • y = x tan θ − gx/(2v cos θ)
  • tm = v0 sin θ0/g; Tf = 2v0 sin θ0/g
  • hm = (v0 sin θ0)2/2g
  • R = v0^2 sin 2θ0/g; Rm = v0^2/g at 45°

Uniform circular motion

  • ac = v2/R = ω2R (towards the centre)
  • ω = Δθ/Δt
  • v = ωR
  • ω = 2π/T = 2πν; ν = 1/T
  • v = 2πR/T = 2πRν
  • ac = 4π2ν2R

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