Finding the Equation of a Perpendicular Plane to a Given Vector 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 for u by 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.
Example: Find the equation of the plane perpendicular to the vector passing through the point
Hence the equation of the plane isNotice the coefficients are the components of the normal vector.