Question

Two non-zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. The angle between them is:

• A. $\pi /4$
• B. $\pi /3$
• C. $\pi /2$
• D. $\pi$

Answer 1

The correct option is C $\pi /2$

Squaring on both sides:
$A^2+B^2+2AB\cos \theta =A^2+B^2-2AB\cos \theta$
$4AB\cos \theta =0or\cos \theta =0or\theta =\frac{\pi }{2}$