If a, b, c, d are coplanar vectors, then (a b) (c d) = - Vidyadip

Question

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

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Answer

d
(d) $(a \times b) \times (c \times d) = [a\,b\,d]c - [a\,b\,c]d$

$\because a,b,c,d$ are coplanar vectors

$\therefore \,\,\,[a\,b\,d] = [a\,b\,c] = 0.$ So, $(a \times b) \times (c \times d) = 0$.

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