How can this vector be ortogonal to the plane
Solution 1:
If $X(x,y,z)$ and $U(u,v,w)$ are two points in the plane, then a vector within the plane is $\overrightarrow{XU}=(u-x,v-y,w-z)$.
You can check that $(3,-1,3)$ is perpendicular to $\overrightarrow{XU}$