Question

If $P=\overrightarrow{A}+\overrightarrow{B}$ and $Q=\overrightarrow{A}-\overrightarrow{B}$ if magnitude of $P$ and $Q$ are equal then angle between $A$ and $B$ is ?

• A. ${180}^o$
• B. ${90}^o$
• C. ${60}^o$
• D. $0^o$

Answer 1

The correct option is B ${90}^o$

Let the angle between two vectors is $\theta$.

$P=\sqrt{A^2+B^2+2AB\cos \theta }$

$Q=\sqrt{A^2+B^2-2AB\cos \theta }$

Since, $P=Q$ therefore,

$\sqrt{A^2+B^2+2AB\cos \theta }=\sqrt{A^2+B^2-2AB\cos \theta }$

$4AB\cos \theta =0$

$\theta ={90}^{\circ }$