Distance Between Two Lines

Distance Between Two Lines

For two intersecting lines:

$$d=0$$

For parallel lines:

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

For skew lines:

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

Usage

- Used to select the appropriate shortest-distance formula based on the relative positions of the lines.