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Motion in A Plane question

2016 · Q141
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Motion in A Plane question

2016 · Q141

NEETPhysicsMotion in A PlaneMCQ+4 / −1
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
  1. A
    45o
  2. B
    180o
  3. C
    0o
  4. D
    90o
View written solutionFree

Correct answer: D

Let the two vectors are A→\overrightarrow A A and B→.\overrightarrow B. B.

Given that, ∣A→+B→∣=∣A→−B→∣\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A - \overrightarrow B } \right|​A+B​=​A−B​

∴\therefore∴ A2+B2+2ABcos⁡θ\sqrt {{A^2} + {B^2} + 2AB\cos \theta } A2+B2+2ABcosθ​ = A2+B2−2ABcos⁡θ\sqrt {{A^2} + {B^2} - 2AB\cos \theta } A2+B2−2ABcosθ​

⇒\Rightarrow⇒ 4ABcos⁡θ{4AB\cos \theta }4ABcosθ = 0

∵\because∵ 4AB{4AB}4AB ≠\ne= 0

∴\therefore∴ cos⁡θ{\cos \theta }cosθ = 0

⇒\Rightarrow⇒ θ\theta θ = 90o

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