Question

$\overrightarrow{A}\cdot (\overrightarrow{A}\times \overrightarrow{B})$ is equal to

• A. $\overrightarrow{A}$
• B. $\overrightarrow{B}$
• C. $0$
• D. $1$

Answer 1

The correct option is C $0$

Let $(\overrightarrow{A}\times \overrightarrow{B})=\overrightarrow{C}$.
$\overrightarrow{C}$ will be perpendicular to both $\overrightarrow{A}$ and$\overrightarrow{B}$.
So, we have $\overrightarrow{A}\cdot (\overrightarrow{A}\times \overrightarrow{B})=\overrightarrow{A}\cdot \overrightarrow{C}=|\overrightarrow{A}||\overrightarrow{C}|\cos {90}^{\circ }=0$