3. Use Stokes's Theorem to evaluate F. dr. For each case, let C be oriented counterclock- G wise when viewed from above. (a) F(x, y. z) = >, C is the triangle with vertices (1, 0,0), (0. 1, 0), and (0, 0, 1) (b) F(x. y. z) =, C is the curve of intersection of the plane 2y + z = 2 and the cylinder x2 + y? = 1 Hint: J F . dr = [f curlF . dS = [fo curlF . (r, xry)dS ; (a) curlF = (2y, 2z,2x) and r, xry = (1, 1, 1). Figure out yourself what S, D, and r are. Ans: (a) 1: (b) 2a