Q. If $\overrightarrow{\mathbf{a}}\mathbf{,}\overrightarrow{\mathbf{b}}\mathbf{,}\overrightarrow{\mathbf{c}}$ are unit coplanar vectors, then $\lbrack 2\ \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}\ 2\overrightarrow{\mathbf{b}}\ - \overrightarrow{\mathbf{c}}\ 2\overrightarrow{\mathbf{c}} - \overrightarrow{\mathbf{a}}\ \rbrack$ is equal to
A) 1
B) 0
C) $- \sqrt{3}$
D) $\sqrt{3}$
Explanation
(b)
$\because$ $\overrightarrow{\mathbf{a}}\mathbf{,}\overrightarrow{\mathbf{b}}\ and\ \overrightarrow{\mathbf{c}}$ are coplanar vectors, so $2\ \overrightarrow{\mathbf{a}}\mathbf{-}\overrightarrow{\mathbf{b}}\ 2\overrightarrow{\mathbf{b}}\ - \overrightarrow{\mathbf{c}}\ and\ 2\overrightarrow{\mathbf{c}}\mathbf{-}\overrightarrow{\mathbf{a}}$ are also coplanar. Thus
$\left\lbrack 2\ \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}\ 2\overrightarrow{\mathbf{b}}\ - \overrightarrow{\mathbf{c}}\ \ 2\overrightarrow{\mathbf{c}}\mathbf{-}\overrightarrow{\mathbf{a}}\ \right\rbrack = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.