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Question

A vector of magnitude 2 coplanar with the vectors a=^i+^j+2^k and b=^i+2^j+^k and perpendicular to the vector c=^i+^j+^k, is


A
j+k
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B
ik
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C
ij
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D
i+k
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Solution

The correct option is A j+k

A vector coplanar with a and b and perpendicular to c is λ((a×b)×c) whose magnitude is 2.
Butλ((a×b)×c)=λ[(ac)b(bc)a]
=λ[4b4a](ac=bc=4)
=4λ[^j^k]
Now, 4|λ|2=2 (Given)
λ=±14
Hence the required vector is ^j^k or ^j+^k


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