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Multiplication with Vectors

Three vectors...

Question

Three vectors satisfy the relation $\to A . \to B = 0$ and $\to A . \to C = 0$ , then $\to A$ is parallel to:

A

\to C

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B

\to B

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C

\to B \times \to C

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D

\to B . \to C

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Solution

The correct option is C $\to B \times \to C$
Using : $\to A \times (\to B \times \to C) = \to B (\to A . \to C) - \to C (\to A . \to B)$
Given : $\to A . \to C = 0$ and $\to A . \to B = 0$
$∴$ $\to A \times (\to B \times \to C) = \to B (0) - \to C (0) = 0$
Thus, $\to A$ is parallel to $(\to B \times \to C)$ .

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