Q. If $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{b}},\overrightarrow{\mathbf{c}}$ 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)
If $\overrightarrow{\mathbf{a}},\overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}\$ are coplanar vectors, then $2\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}},2\overrightarrow{\mathbf{b}} - \overrightarrow{\mathbf{c}}$ and $2\overrightarrow{\mathbf{c}} - \overrightarrow{\mathbf{a}}$ are also coplanar.
$\therefore\left\lbrack 2\overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}}2\ \overrightarrow{\mathbf{b}} - \overrightarrow{\mathbf{c}}\ 2\ \overrightarrow{\mathbf{c}} - \overrightarrow{\mathbf{a}} \right\rbrack = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.