Vectors 3 Question 9
9. If $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ are unit coplanar vectors, then the scalar triple product $[2 \overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}} 2 \overrightarrow{\mathbf{b}}-\overrightarrow{\mathbf{c}} 2 \overrightarrow{\mathbf{c}}-\overrightarrow{\mathbf{a}}]$ is
(2000, 2M)
(a) 0
(b) 1
(c) $-\sqrt{3}$
(d) $\sqrt{3}$
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Answer:
Correct Answer: 9. (a)
Solution:
- If $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}$ 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 vectors.
