Show that on the saddle surface z = xy the two vector fields (VI+ x + /1+y, yvl+x + xv1+y) are principal at each point.

Show that on the saddle surface z = xy the two vector fields (VI+ x + /1+y", yvl+x² + xv1+y) are principal at each point. Check that they are orthogonal and tangent to M.