The distance from a point x0 = (x0, y0, z0) to a plane II in R3 is defined to be

where v := (x0 - x1, y0 - y1, z0 - z1) for some (x1, y1, z1) ˆˆ II, and v is orthogonal to II (i.e., parallel to its normal). Sketch II and xo for a typical plane II, and convince yourself that this is the correct definition. Prove that this definition does not depend on the choice of v, by showing that the distance from x0 = (x0, y0, z0) to the plane II described by ax + by + cz = d is