The angle between the vectors A and B is θ

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The angle between the vectors $\overrightarrow A $ and $\overrightarrow B $ is $\theta .$ The value of the triple product $\overrightarrow A \,.\,(\overrightarrow B \times \overrightarrow A \,)$ is

A

${A^2}B$

B

Zero

C

${A^2}B\sin \theta $

D

${A^2}B\cos \theta $

The angle between the vectors $\overrightarrow A $ and $\overrightarrow B $ is $\theta .$ The value of the triple product $\overrightarrow A \,.\,(\overrightarrow B \times \overrightarrow A \,)$ is

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 $ 

$\therefore\,\overrightarrow A \,.\overrightarrow {\,C} = 0$