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Question

a and b are two vectors such that |a|=1,|b|=4 and ab=2. If c=(2a×b)3b, then the angle between b and c is

A
π3
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B
π6
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C
3π4
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D
5π6
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Solution

The correct option is D 5π6
|a|=1,|b|=4,ab=2,c=(2a×b)3b
c+3b=2a×bab=2cosθ=24=12θ=π3|c+3b|2=|2a×b|2
Taking bc=|b||c|cosα
|c|2+144+6bc=48|c|2+96+6(bc)=0

c=(2a×b)3b
bc=03×16=48

|c|2+966×48=0|c|2=192
Taking bc=|b||c|cosα
192+96+6|b||c|cosα=0cosα=2886×4×83=323=32α=5π6

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