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Question

If a and b are unequal vectors such that (ab)×[(b+a)×(2a+b)]=a+b, then the angle θ between a and b is

A
0
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B
π2
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C
π4
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D
π
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Solution

The correct option is D π
(ab)×[(b+a)×(2a+b)]=a+b

or {(ab)(2a+b)}(b+a){(ab)(b+a)}(2a+b)=b+a

or (2ab1)(b+a)=b+a
either b+a=0 or 1ab=1
either b=a or ab=0
either θ=π or θ=π2

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