Vectors 3 Question 10
10. For three vectors $\overrightarrow{\mathbf{u}}, \overrightarrow{\mathbf{v}}, \overrightarrow{\mathbf{w}}$ which of the following expressions is not equal to any of the remaining three?
(1998, 2M)
(a) $\overrightarrow{\mathbf{u}} \cdot(\overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{w}})$
(b) $(\overrightarrow{\mathbf{v}} \times \overrightarrow{\mathbf{w}}) \cdot \overrightarrow{\mathbf{u}}$
(c) $\overrightarrow{\mathbf{v}} \cdot(\overrightarrow{\mathbf{u}} \times \overrightarrow{\mathbf{w}})$
(d) $(\overrightarrow{\mathbf{u}} \times \overrightarrow{\mathbf{v}}) \cdot \overrightarrow{\mathbf{w}}$
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Answer:
Correct Answer: 10. (c)
Solution:
- $[\overrightarrow{\mathbf{u}} \overrightarrow{\mathbf{v}} \overrightarrow{\mathbf{w}}]=|\overrightarrow{\mathbf{v}} \overrightarrow{\mathbf{w}} \overrightarrow{\mathbf{u}}|=[\overrightarrow{\mathbf{w}} \overrightarrow{\mathbf{u}} \overrightarrow{\mathbf{v}}]=-[\overrightarrow{\mathbf{v}} \overrightarrow{\mathbf{u}} \overrightarrow{\mathbf{w}}]$
Therefore, (c) is the answer.
