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Question

If a,b,c are non-coplanar unit vectors such that ¯a×(¯bׯc)=¯b+¯c2, then the angle between ¯a and ¯b is

A
8π2
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B
π4
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C
π2
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D
π
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Solution

The correct option is B π4
Given ¯a×(¯bׯc)=¯b+¯c2
(¯a¯c)¯b(¯a¯b)¯c=¯b+¯c2
(¯a¯c12)¯b(¯a¯b+12)¯c=¯0
¯a¯c=12 and ¯a¯b=12
(¯a,¯b,¯c are non-coplanar)
cosθ=¯a¯b|¯a|¯b=1/21.1
=12
θ=ππ4
=3π4
angle between ¯a and ¯b is π4

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