Q. $\overrightarrow{\mathbf{a}} \times \left\lbrack \overrightarrow{\mathbf{a}} \times \left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right) \right\rbrack$ is equal to

A) $\left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{a}} \right) \bullet (\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}})$
B) $\overrightarrow{\mathbf{a}} \bullet \left( \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}} \right) - \overrightarrow{\mathbf{b}}(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})$
C) $\lbrack\overrightarrow{\mathbf{a}} \bullet \left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right)\rbrack\overrightarrow{\mathbf{a}}$
D) $\left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{a}} \right)(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}})$
Explanation

(d)
$\overrightarrow{\mathbf{a}} \times \left\lbrack \overrightarrow{\mathbf{a}} \times \left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right) \right\rbrack = \overrightarrow{\mathbf{a}} \times \left\{ \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{a}} - \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{a}} \right)\overrightarrow{\mathbf{b}} \right\}$
$= 0 - \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{a}} \right)(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})$
$= \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{a}} \right)(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}})$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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