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Question

. If a, b, c are three unit vectors such that a×(b×c)=12b then the angles between a, b and a, c are

A
90,90
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B
90,60
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C
60,90
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D
60,30
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Solution

The correct option is B 90,60
Suppose if possible b, c are collinear. Then b×c=0a×(b×c)=012b=0b=0
It is a contradiction to the fact that b is a unit vector. b,c are non collinear.
a×(b×c)=12b(a.c)b(a.b)c=12b(a.c12)b(a.b)c=0
a.c12=0,a.b=0 [Since b, c are not collinear]
a.b=0(a,b)=90
a.c12=0a.c=12|a||c|cos(a,c)=12cos(a,c)=12(a,c)=60

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