Plane Through a Line and a Point

Plane Through a Line and a Point

If a line is:

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

and a point has position vector $$\vec c$$, then a normal vector to the required plane is:

$$\vec n=\vec b\times(\vec c-\vec a)$$

Hence:

$$(\vec r-\vec a)\cdot[\vec b\times(\vec c-\vec a)]=0$$

Usage

- Used to find the unique plane containing a line and a point not on that line.