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Question

If a×(b×c)=(a×b)×c for non-coplanar vectors a, b, c then

A
a parallel to b
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B
b parallel to c
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C
c parallel to a
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D
a+b+c=0
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Solution

The correct option is C c parallel to a
Now, according to the vector cross product rule,
a×(b×c)=(a.c)b(a.b)c................(1)
and
(a×b)×c=(a.c)b(b.c)a ..............(2)
Equating both the equations we get,
(a.b)c=(b.c)a
c is parallel to a.

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