4.2. Plane in space

Let given PDK. The equation sets the plane and is called the general equation of the plane. To write a general equation of the plane, it is necessary to determine the normal vector (the normal of the plane is a straight line perpendicular to the plane) and one point of the plane

Where

If you know the general equation of the plane, then you can easily find the normal equation of the plane:

Where

The plus sign or minus sign is chosen so that p > 0. The angles α, β, γ are the angles between the normal vector n and the axes O x , O y , O z, respectively.

If the normal equation of the plane is known, then it is easy to find the distance ρ from the point to this plane: