HomeHelpContact usBack

Modules Open College - e-Learning Content Library
 
 
The Equation of a Plane in Space.
 


Let α be a plane in space; A0(x0; y0; z0) 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 A0A, therefore, n-A0A=0. Since A0A={õ-x0; y-y0; z-z0}, then {A;B;C}-{õ-x0; y-y0; z-z0}=0, whence

A(õ-x0)+B(y-y0)+C(z-z0)=0

It is the equation of the plane α passing through the given point (x0; y0; z0) 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.



You need to install ActiveX plug-in to be able to view this model.
You can download it here.


 
© OpenTeach Software, 2007