Question

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The triple product $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})$ is equal to.

• A. $A^{2}Bsi{n}^2\theta$
• B. $A^{2}Bsin\theta cos\theta$
• C. $A^{2}Bco{s}^2\theta$
• D. \N

Answer 1

The correct option is D \N

Let $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})=\overrightarrow{A}.\overrightarrow{C}$
Here $\overrightarrow{C}=\overrightarrow{B}\times \overrightarrow{A}$ which is perpendicular to both vector $\overrightarrow{A}$ and $\overrightarrow{B}$
$\therefore \overrightarrow{A}.\overrightarrow{C}=0$