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

The independent vectors $\mathbf{a},\mathbf{b}$ span the plane through the origin, and their cross product is a nonzero normal vector. Thus the required nonparametric equation is

The orientation assumption gives $\mathbf{c}\cdot (\mathbf{a}\times \mathbf{b})>0$. The same open half-space is therefore characterized byEquality would put the point in the separating plane, rather than strictly on the same side.