# Difference between revisions of "Plane"

File:Plane.png
Figure 1. A plane is the intersection of a 4D trivector with the 3D subspace where $$w = 1$$.

In the 4D projective geometric algebra $$\mathcal G_{3,0,1}$$, a plane $$\mathbf f$$ is a trivector having the general form

$$\mathbf f = f_x \mathbf e_{234} + f_y \mathbf e_{314} + f_z \mathbf e_{124} + f_w \mathbf e_{321}$$ .

All planes possess the geometric property.

A plane is unitized when $$f_x^2 + f_y^2 + f_z^2 = 1$$.

When used as an operator in the sandwich product, a unitized plane is a specific kind of flector that performs a reflection through itself.