IIT-JEE 2011 · Paper 1, Mathematics question 54

Coplanar vectors are $\lambda(1,1,2)+\mu(1,2,1)$; perpendicular to $(1,1,1)$ means $4\lambda+4\mu=0$.

So $\vec v\propto(1,1,2)-(1,2,1)=(0,-1,1)$: both $\hat j-\hat k$ and $-\hat j+\hat k$.

(A), (D)