Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 2 / 11 / d / Solution

The opposite face lies in the plane spanned by $\mathbf{a},\mathbf{b}$ through the origin. Directly,The distance from a point to a plane is the absolute normal component, soHere $\mathbf{c}=(\mathbf{a}\times \mathbf{b})/2$, so the perpendicular foot is the origin, a vertex of the opposite triangular face. Thus the distance to the actual face equals the distance to its containing plane.