Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 2 / 11 / d / i

For a point $\mathbf{p}={\mathbf{r}}_2(t)$, the magnitude of $(\mathbf{p}-{\mathbf{a}}_1)\times {\mathbf{n}}_1$ is the area of a parallelogram. Dividing by its base length $\Vert {\mathbf{n}}_1\Vert$ gives the perpendicular Euclidean distance to the first line. Explicitly,HenceThis use of the cross product removes any component parallel to the first line automatically.