Past exam of the mathematical methods I course of the University of Oxford / 2017 resit / 8 / b

The plane has normal vector $\mathbf{n}=(2,3,6)$ of length seven. Projecting the displacement from any point on the plane onto the unit normal gives the distance from a point to a planeFor example the perpendicular foot is ${\mathbf{r}}_0-\mathbf{n}(\mathbf{n}\cdot {\mathbf{r}}_0-30)/49$. Substitution places it on the plane, and its displacement from ${\mathbf{r}}_0$ is parallel to $\mathbf{n}$, verifying that this is the minimum distance.