Question

For two non zero vectors $A$ and $B$, if $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$ then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\pi$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\pi$

We know that $\overrightarrow{A}\times \overrightarrow{B}=-(\overrightarrow{B}\times \overrightarrow{A})$
But if the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is integer multiple of $\pi$.
Then $\overrightarrow{A}\times \overrightarrow{B}\times =\overrightarrow{B}\times \overrightarrow{A}=0.$