Q. If $\overrightarrow{\mathbf{b}}$ is a unit vector, then $\left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{b}} \times (\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})$is
A) $|\overrightarrow{\mathbf{a}}|^{2}\overrightarrow{\mathbf{b}}$
B) $|\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|\overrightarrow{\mathbf{a}}$
C) $\overrightarrow{\mathbf{a}}$
D) $\overrightarrow{\mathbf{b}}$
Explanation
(c)
$\left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{b}} \times \left( \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right)$
$= \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{b}} + \left( \overrightarrow{\mathbf{b}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{a}} - \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} \right)\overrightarrow{\mathbf{b}}$
$= \overrightarrow{\mathbf{a}}\ \ \ \ \ \lbrack\because|\overrightarrow{\mathbf{b}}| = 1\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.