Question

Given $\overrightarrow{P}=\overrightarrow{A}+\overrightarrow{B}$ and $\overrightarrow{Q}=\overrightarrow{A}-\overrightarrow{B}$. If the magnitudes of vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ are equal, what is the angle between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$?

• A. zero
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is C

$\frac{\pi }{2}$

Let $\theta$ be the angle between A and B. Then magnitudes of vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ are given by
$P=\sqrt{A^2+B^2+2ABcos\theta }$
and $Q=\sqrt{A^2+B^2-2ABcos\theta }$
Since P = Q, it follows that $cos\theta =0$ or $\theta =\frac{\pi }{2}$.
Hence, the correct choice is (c).