Vector that is orthogonal to one vector in a plane, automatically the normal? I'm trying to understand why if a vector is orthogonal to one vector in a plane, why it wouldn't be orthogonal to all vectors in that plane? 
Sketches/diagrams would be helpful.

Think of the $xy$-plane in $\mathbb{R}^3$ and the vector $\hat{\text{i}}$. $\hat{\text{j}}$ is orthogonal to $\hat{\text{i}}$ but it's not orthogonal/normal to the plane.
