Need some help on this calculus 3 question.

Question

Let f (x, y) = √xy + xy. Let S be the surface z = f (x, y) Let P be the point on S (1, 1, f (1, 1)) and let Q be the point on S (16, 4, f (16, 4)). Find parametric equations for the line of intersection of the tangent planes at the

points P and Q.

Answer 1

It's a lot of typing but, in general, find the del S at point P then again at Point Q. This will result in equations of the tangent planes. Next find the cross product of the two planes that will yield the direction vector V which is part of the parametric equation for L=L₀ +tV where t is the parameter. Find L0 by solving for an intersection point of the two planes algebraically.