Q. The vector $\overrightarrow{\mathbf{a}} \times (\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})$ is coplanar with the vectors
A) $\overrightarrow{\mathbf{b}},\overrightarrow{\mathbf{c}}$
B) $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{b}}$
C) $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{c}}$
D) $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{b}},\overrightarrow{\mathbf{c}}$
Explanation
(a)
Since, $\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}$ is a vector perpendicular to $\overrightarrow{\mathbf{b}},\overrightarrow{\mathbf{c}}.$ Therefore $\overrightarrow{\mathbf{a}} \times (\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})$ is a vector again in plane of $\overrightarrow{\mathbf{b}},\overrightarrow{\mathbf{c}}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.