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Question

If αa+βb+γc=0, then (a×b)×{(b×c)×(c×a}=

A
0
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B
Avector perpendicular to the plane of a,b, c
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C
A scalar quantity
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D
2[a b c]
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Solution

The correct option is A 0
Solving
=a×b×((b×ca)c(a×cc)a)
=a×b×c(b×ca)
=((ac)b(ab)c)[abc]-----(1)
Now
αa+βb+γc=0
=αa×c+βb×c=0
=βb×ca=0
[bca]=0-----(2)

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