1. (Problem Set 35, #1) (a) One of the following two vector fields is path-independent. Which one, and how do you know? i. F(x, y, z) = (3x2, sin z, y cos z + e2y) ii. F(x, y, 2) = (3x2 + zey, sin z + xzey, xey + y cos z + 2") (b) Find a potential function for the path-independent vector field in #1(a), and explain how you found it. (Remember that a potential function for a vector field F is a function f such that Vf = F.) (c) For the path-independent vector field F in #1(a), evaluate F . dr where C is the curve param- eterized by r(t) = (t, t2, t3 ) from t = 0 to t = 1