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Question

If a×(b×c)+b×(c×a)+c×(a×b)=x×y then

A
x and y are parallel
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B
x=0
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C
x=0 or y=0 or x and y are parallel
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D
(y)=0
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Solution

The correct option is B x=0 or y=0 or x and y are parallel
We know that a×(b×c)=(a.c).b(a.b).c
b×(c×a)=(b.a).c(b.c).a
c×(a×b)=(c.b).a(c.a).b
And a.b=b.a b.c=c.b and a.c=c.a
Using the above relations we have
a×(b×c)+b×(c×a)+c×(a×b)=(a.c).b(a.b).c+(b.a).c(b.c).a+(c.b).a(c.a).b
=0
x×y=0
x is parallel to y
and x=0 or y=0

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