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If $a, b, c$ are coplanar vectors then
$(a \times b) \times (b \times c) + (b \times c) \times (c \times a) + (c \times a) \times (a \times b) =$

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$0$

$a + b + c$

$[a b c]$

$[a b c] (a + b + c)$

answer is C.

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Detailed Solution

$\begin{array}{rcl} = & [a b c] b - 0 + [b c a] c - 0 + [c a b] a - 0 \\ = & [a b c] b + [a b c] c + [a b c] a \\ = & [a b c] [a + b + c] \end{array}$

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