Plane Through a Given Line

Plane Through a Given Line

If a line is:

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

then any plane containing this line has a normal vector $$\vec n$$ satisfying:

$$\vec n\cdot\vec b=0$$

and its equation can be written as:

$$(\vec r-\vec a)\cdot\vec n=0$$

Usage

- Used to construct a plane containing a specified line.