If and are two unit vectors then the vector x x is parallel to ........

Mathematics (NDA) Vector

If $\hat{a}$ and $\hat{b}$ are two unit vectors, then the vector ( $\hat{a}$ + $\hat{b}$ )x( $\hat{a}$ x $\hat{b}$ ) is parallel to?

( $\hat{a}$ - $\hat{b}$ )

( $\hat{a}$ + $\hat{b}$ )

(2 $\hat{a}$ - $\hat{b}$ )

(2 $\hat{a}$ + $\hat{b}$ )

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Explanation:

( $\hat{a}$ + $\hat{b}$ )x( $\hat{a}$ x $\hat{b}$ )= $\hat{a}$ x( $\hat{a}$ x $\hat{b}$ )+ $\hat{b}$ ( $\hat{a}$ x $\hat{b}$ )
=( $\hat{a}$ - $\hat{b}$ ) $\hat{a}$ -( $\hat{a}$ . $\hat{a}$ ) $\hat{b}$ +( $\hat{b}$ . $\hat{b}$ ) $\hat{a}$ -( $\hat{b}$ . $\hat{a}$ ) $\hat{b}$
=k $\hat{a}$ - $\hat{b}$ + $\hat{a}$ -k $\hat{b}$
=(k+1)( $\hat{a}$ - $\hat{b}$ )