A plane has equation x- 2y +z = 4. Show that the square, say D^2, of the distance from the point P = (-1,3,2) to a point (x,y,z) on the plane is given by
D^2 = 2x^2 - 2x + 14 + 5y^2 + 2y - 4xy.
By finding the minimum of D^2 determine the shortest distance from P to the plane. (You should verify that the distance is indeed a minimum.) Let Q be the point on the plane clasest to P. Show that the line QP is perpendicular to the plane at Q.