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Question

Let a=^i+^j; b=2^i^k. Then, vector r satisfying the equations r×a=b×a and r×b=a×b is

A
^i^j+3^k
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B
3^i^j+^k
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C
3^i+^j^k
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D
^i^j^k
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Solution

The correct option is C 3^i+^j^k
r×a=b×a and r×b=a×b

r×a=(r×b)
r×(a+b)=0
r=λ(a+b)
[ angle between them is 0]
r=λ(^i+^j+2^i^k)
r=λ(3^i+^j^k)
If λ=1, then
r=3^i+^j^k

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