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Question

If a and c are perpendicular vectors then any vectors b, the vectors a×(b×c) and (a×b)×c are

A
perpendicular
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B
parallel
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C
each equal to 0
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D
parallel respectively to a and b
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Solution

The correct option is A perpendicular
Given, a and ¯c are perpendicular vector

then, a×c=1 or ac=0
a×(b×c)
(ac)b(ab)c
(ab)c(i)ac=0
now, (a×b)×C
(ca)b(bc)a
(bc)a(ii)ac=0
Now, doing dot produt of vector in equation (i) and (ii), We get,
a×(¯b×c)(¯aׯb)c=(¯ab)(bc)ca
Both vectors are perpendicular
option A= perpendicular


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