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Question

If a,b and c are non coplanar unit vectors such that a×b×c=b+c2 then the angle between

A
a & b is 3π4
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B
a & b is π4
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C
a & c is 3π4
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D
a & c is π4
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Solution

The correct options are
A a & b is 3π4
D a & c is π4
a×(b×c)=b+c2
(a.c)b(a.b)c=b2+c2
(a.c12)b(a.b+12)c=0
a.b=12 and a.c=12
Hence
Angle between a and b is cos1(12)=3π4
And angle between a and c is cos1(12)=π4

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