[Question] Hi, my teacher gave us this problem, and he couldn't figure out why method was incorrect and why I got the answer I did. Given we know the gradient slope = <-56,1.886> at the point (2,0) on a surface f(x,y), in what direction, expressed as a unit vector, is f increasing most rapidly? [Difficulty] I solved the problem like this: Max slope = magnitude of gradient slope (gradient slope) dot (unit vector) = 56.03 -56.03Ux + 1.866Uy = 56.03 sqt(Ux^2 + Uy^2) = 1 Solving the system Ux= -.9977 Uy=.0672 The only problem is, by definition, I should be able to get the unit vector by taking the gradient slope vector and dividing by the magnitude of the gradient vector. or, <-56/56.03, 1.886/56.03> = <Ux,Uy> = <-.9994,.0336> The weird thing is, the correct Uy value is almost exactly half of mine...what's going on??? [Thoughts] I tried a similiar technique for finding where the ∇f = 0 <-56, 1.866> dot (unit vector) = 0 -56.03Ux + 1.886Uy = 0 sqt(Ux^2 + Uy^2) = 1 Solving the system this time I got the correct answer, why here and not there?