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. $[2 \overrightarrow{ a }-\overrightarrow{ b } 2 \overrightarrow{ b }-\overrightarrow{ c } 2 \overrightarrow{ c }-\overrightarrow{ a }]=0$