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Question

Three vectors a, b, c are such that a×b=4(a×c) and |a|=|b|=1 and |c|=14. If the angle between b and c is π3, then b is

A
a+4c
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B
a4c
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C
4ca
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D
2ca
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Solution

The correct options are
A a+4c
C 4ca
a×b=4(a×c)
a×b=(a×4c)
a×b(a×4c)=0
a×(b4c)=0
So, a and (b4c) are collinear or parallel vectors.
λa=(b4c) [1]
|λa|2=|b4c|2
λ2|a|2=|b|2+16|c|28×(bc)
λ=±1

Putting λ=1 in [1], we get
b=4c+a

Putting λ=1 in [1], we get
b=4ca

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