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Question

The unit vector which is orthogonal to the vector 3^i+2^j+6^k and is coplanar with the vectors 2^i+^j+^k and ^i^j+^k

A
2^i6^j+^k41
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B
2^i3^j13
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C
3^j^k10
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D
4^i+3^j3^k34
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Solution

The correct option is C 3^j^k10
As we know that, a vector coplanar to a,b and orthogonal to c is λ(a×b)×c.
A vector coplanar to (2^i+^j+^k),(^i^j+^k) and orthogonal to 3^i+2^j+6^k=λ[{(2^i+^j+^k)×(^i^j+^k)}×(3^i+2^j+6^k)]=λ[(2^i^j3^k)×(3^i+2^j+6^k)]=λ(21^j7^k) Unit vector=+(21^j7^k)(21)2+(7)2=+(3j^k)10


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