Find the unit vector orthogonal to the vector 3i+2j+6k and coplanar with the vectors 2i+j+k and i-j+k.

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Please find below the solution to the asked query:

3,2,6Let the desired vector be A=ai^+bj^+ck^Now if three vectors are coplanars then one vector can be written as linear sum ofother two.ai^+bj^+ck^=2i^+j^+k^+λi^-j^+k^ai^+bj^+ck^=2+λi^+1-λj^+1+λk^Now ai^+bj^+ck^ is orthogonal to 3i^+2j^+6k^, hence their dot product will be 0.ai^+bj^+ck^.3i^+2j^+6k^=02+λi^+1-λj^+1+λ.3i^+2j^+6k^=032+λ+21-λ+61+λ=06+3λ+2-2λ+6+6λ=07λ=-14λ=-22+λi^+1-λj^+1+λk^=2-2i^+1+2j^+1-2k^A=3j^-k^A^=3j^-k^32+-12=3j^-k^9+1A^=3j^-k^10

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