Question

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are unit coplanar vectors, then the scalar triple product $[2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}]$ is

• A. 0
• B. 1
• C. $-\sqrt{3}$
• D. $\sqrt{3}$

Answer 1

Answer: (A)

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are coplanar vectors, then $2\overrightarrow{a}-\overrightarrow{b},2\overrightarrow{b}-\overrightarrow{c}$ and $2\overrightarrow{c}-\overrightarrow{a}$ are also coplanar vectors.
i.e. $[2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}]=0$