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Motion in a Plane · Class 11 · CBSE · Science Physics

If the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between the two vectors?

Practice question from Motion in a Plane (Class 11 · CBSE · Science Physics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-35A2E8

If the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between the two vectors?

  1. A.0∘0^\circ
  2. B.45∘45^\circ
  3. C.90∘90^\circCorrect answer
  4. D.180∘180^\circ

Solution

Given ∣A⃗+B⃗∣=∣A⃗−B⃗∣|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|. Squaring both sides: A2+B2+2ABcos⁡θ=A2+B2−2ABcos⁡θA^2 + B^2 + 2AB\cos\theta = A^2 + B^2 - 2AB\cos\theta, which implies 4ABcos⁡θ=04AB\cos\theta = 0. Since A≠0A \neq 0 and B≠0B \neq 0, cos⁡θ=0\cos\theta = 0, so θ=90∘\theta = 90^\circ.

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