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Question

Let a and b be 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
π6
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B
π3
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C
5π6
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D
2π3
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Solution

The correct option is C 5π6
Given, |a|=1, |b|=4 and ab=2.
|a×b|2=|a|2|b|2(ab)2
|a×b|2=164=12

Now, c=2a×b3b
|c|2=4|a×b|2+9|b|2
|c|2=4×12+9×16=192

c=(2a×b)3b
Taking dot product with c, we get
bc=03|b|2=48

Let θ be the angle between b and c.
Then, cosθ=bc|b||c|
cosθ=484×83=32
θ=5π6

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