Plane

A mathematical plane is a 2-dimensional surface defined by a normal vector that the plane is perpendicular to.

Cartesian Form §

The cartesian equation of a plane is that of the form: $ax+by+cz=d$ where $a,b,c,d$ are constants

The vector $\mathbf{n}=a\mathbf{i}+b\mathbf{j}+c\mathbf{k}$ is the normal vector to the plane.

$d$ can also be defined as $\mathbf{n}\cdot a_0$ where $a_0$ is the a point on the plane.