Plane Through a Line and Perpendicular to Another Plane

Plane Through a Line and Perpendicular to Another Plane

If a required plane contains a line with direction vector $$\vec d$$ and is perpendicular to a plane with normal vector $$\vec n$$, its normal vector $$\vec N$$ satisfies:

$$\vec N\cdot\vec d=0$$

and:

$$\vec N\cdot\vec n=0$$

Hence:

$$\vec N\parallel\vec d\times\vec n$$

Usage

- Used to construct a plane containing a line and perpendicular to another plane.