Vectors 3 Question 26
26. If $\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{A}}=0, \overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{B}}=0, \overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{C}}=0$ for some non-zero vector $\overrightarrow{\mathbf{X}}$, then $[\overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} \overrightarrow{\mathbf{C}}]=0$.
(1983, 1M)
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Answer:
Correct Answer: 26. True
Solution:
- Since, $\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{A}}=\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{X}} \cdot \overrightarrow{\mathbf{C}}=\mathbf{0}$
$\Rightarrow \overrightarrow{\mathbf{X}}$ is perpendicular to $\overrightarrow{\mathbf{A}}, \overrightarrow{\mathbf{B}}, \overrightarrow{\mathbf{C}}$, therefore $[\overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} \overrightarrow{\mathbf{C}}]=0$
Hence, given statement is true.
