Q. If $\overrightarrow{\mathbf{a}}$ is vector perpendicular to both $\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{c}}$ then
A) $\overrightarrow{\mathbf{a}} + (\overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}}) = \overrightarrow{\mathbf{0}}$
B) $\overrightarrow{\mathbf{a}} \times (\overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}}) = \overrightarrow{\mathbf{0}}$
C) $\overrightarrow{\mathbf{a}} \times (\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}) = \overrightarrow{\mathbf{0}}$
D) $\overrightarrow{\mathbf{a}} \bullet (\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}) = \overrightarrow{\mathbf{0}}$
Explanation
(c)
$\overrightarrow{\mathbf{a}} \times \left( \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}} \right) = \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{c}} \right)\overrightarrow{\mathbf{b}} - \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{c}} = \overrightarrow{0},$
$\lbrack\because\overrightarrow{\mathbf{a}}\bot\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{a}}\bot\overrightarrow{\mathbf{c}}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.