Q. The vector $\overrightarrow{\mathbf{c}} \bullet \left( \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}} \right) \times (\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}})$ is equal to
A) $\overrightarrow{\mathbf{c}} \bullet \ \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}$
B) $\overrightarrow{\mathbf{0}}\$
C) $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}$
D) $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{b}}$
Explanation
(a)
$\overrightarrow{\mathbf{c}} \bullet \left( \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}} \right) \times \left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} + \overrightarrow{\mathbf{c}} \right)$
$= \overrightarrow{\mathbf{c}} \bullet \left( \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}} + \overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{b}} \right)$
$= \overrightarrow{\mathbf{c}} \bullet \overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.