FindinThe Perpendicular Line to a Plane Passing Through a Given Point

If a vectoris perpendicular to a planethen it is perpendicular to every vectorand line drawn in the plane, henceWe can find an expression forby subtracting one point in the plane from another. This is shown on the diagram above aswhereis an arbitrary point andis given, so by findingor we find the equation of the plane. Hence if the equation of a plane isa normal is given byIf the normal is to pass through the pointthen the line can be written:

Example: Find the equation of the plane perpendicular to the plane 2x-4y-3z=17 passing through the point