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Multiplication with Vectors

If A and B ar...

Question

If $\to A$ and $\to B$ are two non-zero vectors, then the value of $(\to A \times \to B) \times (\to A - \to B)$ is

A

0

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B

A^{2} - B^{2}

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C

\to B \times \to A

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D

2 (\to B \times \to A)

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Solution

The correct option is D $2 (\to B \times \to A)$
$(\to A + \to B) \times (\to A - \to B)$
$= \to A \times (\to A - \to B) + \to B \times (\to A - \to B)$
$= \to A \times \to A - \to A \times \to B + \to B \times \to A - \to B \times \to B$
$= \to B \times \to A + \to B \times \to A$
$= 2 (\to B \times \to A)$

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