(a→×b→)×(b→×c→)=

(a×b)×(b×c) =(a×b·c) b-(a×b·b) c =[a b c] b

(a×b)×(b×c) =(a×b·c) b-(a×b·b) c =[a b c] b

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$(\vec{a} \times \vec{b}) \times (\vec{b} \times \vec{c}) =$

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$[\vec{a} \vec{b} \vec{c}] \vec{a}$

$[\vec{a} \vec{b} \vec{c}] \vec{b}$

$[\vec{a} \vec{b} \vec{c}] \vec{c}$

$[\vec{a} \vec{b} \vec{c}]$

answer is B.

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$\begin{array}{rcl} (a \times b) \times (b \times c) \\ = & (a \times b \cdot c) b - (a \times b \cdot b) c \\ = & [a b c] b \end{array}$

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