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Question

If |a|=1, |b|=4,a.b=2 and c=2a×b3b, then the angle between b and c is?


A

π6

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B

5π6

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C

π3

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D

2π3

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Solution

The correct option is B

5π6


Explanation for the correct option:

Step 1. Find the value of |c|:

Given, |a|=1,|b|=4,a.b=2 and c=2a×b3b

We now that |a×b|2=|a|2|b|2-(a.b)2

|a×b|2=16-4=12

And given that c=2a×b3b

|c|2=(2a×b-3b)2

|c|2=4|a×b|2+9|b|2

|c|2=4(12)+9(16)

|c|2=192

|c|=83

Step 2. Find the angle between b and c :

We have b.c=b(2a×b3b)

b.c=-3|b|2

b.c=-48

The angle between b and c is given by cosθ=(b.c)(|b||c|)

cosθ=-48(4×83)cosθ=-32θ=cos-1-32θ=5π6

Hence, the correct option is (B).


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