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Vector component of $b$ perpendicular to $a$ is

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$(b . c) a$

$\frac{a \times (b \times a)}{{|a|}^{2}}$

$\frac{(b . c) . a}{{|a|}^{2}}$

$a \times (b \times a)$

answer is B.

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Detailed Solution

Vector $\begin{array}{rcl} = & b - \frac{(b \cdot a) a}{| a |^{2}} \end{array}$

$\begin{array}{rcl} = & \frac{| a |^{2} b - (b \cdot a) a}{| a |^{2}} \\ = & \frac{a \times (b \times a)}{| a |^{2}} \end{array}$

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