Distance Between Two Lines

Topics: Geometry - Line - 3D Space

---

Let $l_1=\{p+tu:t\in \mathbb{R}\}$ and $l_2=\{q+sv:v\in \mathbb{R}\}$ be lines in ${\mathbb{R}}^3$.

The distance between $l_1$ and $l_2$ is given by:

$$\text{d}(l_1,l_2)=\frac{|(p-q)\cdot (u\times v)|}{\Vert u\times v\Vert }$$