Consider a plane II whose unit normal vector pointing outward from the origin is n = ai+ bj+ck and the shortest distance from the origin O(0,0,0) is d, as shown in the figure. Show that all points P(x,y,z) on this plane satisfy the equation ax+ by+cz– d=0. •P d 1=

Find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P(x Yo z), and a vector n = (a, b, c) that is parallel to the line. Then the equation of the line is x - xo = at, y - Yo = bt, z - zo = ct.) x2 - 9xyz + y + 7z = 0, P(1, 1, 1)