(2) (15pt) Suppose S is a regular surface. We say a curve a : I S is the gradient curve of a differentiable function f defined on R3 if it satisfies the equation o(t) = (Vf(a)', where Vf is the gradient vector of f defined on R?, and T means the projection of the vector of V f((t)) to the tangent space Ty)S. Show that for any p S, there exists > 0 and a gradient curve a : (,) S such that a(0) = p