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Question

Let a=^i+^j & b=2^i+^j The point of intersection of the lines r×a=b×a&r×b=a×b is

A
^i+^j+^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 B 3^i+^j^k
a=^i+^j & ^b=^2i^kr×a=b×a(rb)×a=0r=b+λa
Similarly r×b=a×br=a+μb
Substitute the vector a & b in (i) & (ii) and equating we get
2^i^k+λ(^i+^j)=^i+^j+μ(2^i^k)2+λ=1+2μ,λ=1,μ=1 Point of intersection is 3^i+^j^k

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