Use stokes' theorem to compute z c ~f d~s where ~f(x; y; z) = y2~i + z2~j + x~k and the curve c is the triangle in 3-space with vertices at (1; 0; 0), (0; 1; 0), and (0; 0; 1). hints: (a) for the surface s needed in stokes' theorem, use the part of the plane x + y + z = 1 that lies in the rst octant. (b) that plane can be written parametrically as (x; y) = hx; y; 1 x yi. (c) make sure you have the upward pointing normal!