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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


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


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

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