Assume perfect sphere lands on a surface given by the function z = 2x2 -3y2 at point (2,1,5). I am trying to find a unit vector of the direction in which this perfect sphere will roll. If I get grad F I'll get a vector field that is perpendicular to the level curves f(x,y) = z = 2x2 -3y2. This is going to be the steepest ascent. Thus negative grad F should give the steepest descent. However, this is still a normal to the level surface. How do I find the direction in which it will roll along the surface? PS. this is not a homework question. I was studying some differential geometry over the holidays and this problem was given in the book.