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Question

If 4a+5b+9c=0, then (a×b)×[(b×c)×(c×a)] is equal to

A
a vector perpendicular to the plane of a, b and c
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B
a scalar quantity
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C
0
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D
Vector quantity
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Solution

The correct option is B 0
Let, 4a+5b+9c=0......(1).
Now, (a×b)×[(b×c)×(c×a)]
=(a×b)×[{(b×c).a}c{(b×c).c}a].
=(a×b)×[bca]c [Since, [bcc]=0]
=0.
As, [bca]
=[abc]
=(a×b).(49a59b) [Using (1)]
=49[aba]59[abb]
=0.

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