Question

If $\overrightarrow{A}and\overrightarrow{B}$ are two vectors such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. The angle between them in radians is

• A. $\pi /4$
• B. $\pi /6$
• C. $\pi /2$
• D. $\pi$

Answer 1

The correct option is C $\pi /2$

$|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$

$\Rightarrow \sqrt{A^2+B^2+2ABcos\theta }=\sqrt{A^2+B^2-2ABcos\theta }$

From this equation we get:

$\Rightarrow ABcos\theta =0$

$\Rightarrow \theta =\frac{\pi }{2}$

The angle between two vectors A and B is $\frac{\pi }{2}$.