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AIIMS 2016
Exam
AIIMS
Year
2016
Subject
Physics
Chapter
Mathematics in Physics

AIIMS 2016 · Physics · Mathematics in Physics

If A and B are non-zero vectors which obey the relation | A + B |=|...

If A⃗\vec{A} and B⃗\vec{B} are non-zero vectors which obey the relation ∣A⃗+B⃗∣=∣A⃗−B⃗∣|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|, then the angle between them is

Options

  1. A0∘0^{\circ}
  2. B60∘60^{\circ}
  3. C90∘90^{\circ}
  4. D120∘120^{\circ}

Correct answer

C. 90∘90^{\circ}

Step-by-step solution

 ∣A⃗+B⃗∣=∣A⃗−B⃗∣∣A⃗∣2+∣B⃗∣2+2∣A⃗∣∣B⃗∣cos⁡θ=∣A⃗∣2+∣B⃗∣2−2∣A⃗∣∣B⃗∣cos⁡θ∴cos⁡θ=0⇒θ=90∘\begin{aligned} \text{ } & |\vec{A}+\vec{B}|=|\vec{A}-\vec{B}| \\ & |\vec{A}|^2+|\vec{B}|^2+2|\vec{A}||\vec{B}| \cos \theta \\ & =|\vec{A}|^2+|\vec{B}|^2-2|\vec{A}||\vec{B}| \cos \theta \\ \therefore & \cos \theta=0 \Rightarrow \theta=90^{\circ}\end{aligned}
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