Question

If $\overrightarrow{P}$ and $\overrightarrow{Q}$ are two non-zero vectors, what is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$ ?

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

Answer 1

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

Vector $(\overrightarrow{P}+\overrightarrow{Q})$ lies in a plane of $\overrightarrow{P}$ and $\overrightarrow{Q}$ and vector $(\overrightarrow{P}\times \overrightarrow{Q})$ is perpendicular to this plane. Thus the angle between given vectors is $\frac{\pi }{2}$