Let **α **be a plane in space; **A**_{0}(x_{0}; y_{0}; z_{0}) and **A(x;y;z)** be any points of the plane **α**; vector **n={A;B;C}** is a vector normal to the plane **α**, that is **n** is perpendicular to the **α** and **n** is perpendicular to the segment **A**_{0}A, therefore, **n-A**_{0}A=0. Since **A**_{0}A={õ-x_{0}; y-y_{0}; z-z_{0}}, then **{A;B;C}-{õ-x**_{0}; y-y_{0}; z-z_{0}}=0, whence

**A(õ-x**_{0})+B(**y-y**_{0})+C(z-z_{0})=0

It is the equation of the plane **α** passing through the given point **(x**_{0}; y_{0}; z_{0}) and having the given normal vector **{A; B; C}**. After removing the brackets and several simplifications we obtain the general **equation of a plane**

**Ax+By+Cz+D=0**.

The coordinate planes **xOy**, **xOz**, **yOz** have correspondingly the equations **z=0**, **y=0**, **x=0**.