The correct option is C 3^j−^k√10
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−^j−3^k)×(3^i+2^j+6^k)]=λ(21^j−7^k)∴ Unit vector=+(21^j−7^k)√(21)2+(7)2=+(3→j−^k)√10