Shortest Distance Between Two Skew Lines

Shortest Distance Between Two Skew Lines

For lines:

$$\vec r=\vec a+\lambda\vec b$$

and:

$$\vec r=\vec c+\mu\vec d$$

the shortest distance is:

$$D=\frac{|(\vec c-\vec a)\cdot(\vec b\times\vec d)|}{|\vec b\times\vec d|}$$

Terminology

- Skew lines: Lines that are neither parallel nor intersecting and do not lie in the same plane.

Usage

- Used to find the shortest distance between two non-parallel, non-intersecting lines.