please solve problem attached and show all work, thanks

10. (16 points) A metal surface S in R3 is given by a continuously differentiable vector function r(u, v) = (33(u,v),y(u,v),z(u, 11)) for (um) in [1,1] x [1,1]. The temperature at each point (33, y, z) on S is equal to T(:r:, y, z), where T is a continuously differentiable function. Assume that the maximimum temperature on 8 occurs at the point (55(0, 0), y(0, 0), 2(0, 0)) = (1, 2, 3). Show that the gradient VT(1, 2, 3) is parallel to the vector ru(0, 0) X rum, 0)