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If $(a \times b) \times (c \times d) = p a + q b$ where $a, b$ are non-collinear and $c, d$ are also non-collinear, then

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$p = [c b d]$

$p = [\begin{array}{lll} a c d \end{array}]$

$p = [a b d]$

$p = [a b c]$

answer is A.

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Detailed Solution

$\begin{array}{l} (a \times b) \times (c \times d) \\ = (a \cdot (c \times d)) b - (b \cdot (c \times d)) a \\ = p a + q b \end{array}$

So $\begin{array}{l} p = - (b \cdot (c \times d)) = b \cdot (d \times c) = [b d c] \\ = [c b d] . \end{array}$

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