Given that c is in the plane of a, b and d is not in the plane of a, b then (a×b)×(c×d)=

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Given that $c$ is in the plane of $a, b$ and $d$ is not in the plane of $a, b$ then $(a \times b) \times (c \times d) =$

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parallel to $b$

in the plane of $a, b$ but not in the plane of $c, d$

parallel to $c$

parallel to $a$

answer is C.

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Detailed Solution

$\begin{array}{rcl} [c a b] & = & 0 [d a b] \neq 0 \\ (a \times b) \times (c \times d) & = & [a b d] c - [a b c] d \end{array}$

$= [a b d] c \Rightarrow$ Parallel to $c$

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