May I have all parts of the question answered with full working, all formulas used and typed.
Consider the surface given by the equation xy2 + x2 z + yz2 = 7.
(a) Find an equation for the tangent plane to the surface at the point (1, 1, 2). Graph the surface and the tangent plane with a good view of tangency.
(b) Find all points where the tangent plane to the surface is parallel to the plane z = 3x + y.
(c) Find the symmetric equations for the normal line to the surface at the point (1, 1, 2).