Past exam of the mathematical methods I course of the University of Oxford / 2014 resit / 9 / Solution

Normalize the normal vector $(2,4,3)$, whose Euclidean norm is $\sqrt{29}$. The plane has the formThe scalar $d$ is the signed perpendicular distance from the origin in the chosen unit normal direction; the unsigned distance is $|d|$. The nearest point is $d\mathbf{n}$.