plane from point and normal vector

Given a point $(x_0,y_0,z_0)$ and normal vector $\vec{n}$, a plane can be defined as follows:

$$\begin{array}{rl}{n}_x(x-x_0)+n_y(y-y_0)+n_z(z-z_0)& =0\\ n_x\cdot x+n_y\cdot y+n_z\cdot z& =n_x\cdot x_0+n_y\cdot y_0+n_z\cdot z_0\end{array}$$