Question

Two non - zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. Find angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

• A. $0^{\circ }$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is C $\frac{\pi }{2}$

According to question,
$|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$
$\Rightarrow A^2+B^2+2AB\cos \theta =A^2+B^2-2AB\cos \theta$
$\Rightarrow 4AB\cos \theta =0$
$\Rightarrow \cos \theta =0$
$\Rightarrow \theta =\frac{\pi }{2}$