Begin with the paraboloid z = x2 + y?, for 0 sz$64, and slice it with the plane y = 0. Let S be the surface that remains for y 2 0 (including the planar surface in the xz-plane) (see figure). Let C be the semicircle and line segment that bound the cap of S in the plane z = 64 with counterclockwise orientation. Let F = (4z + 3y, 4x + 3z, 4y + 3x) . Complete parts (a) through (c) below. 641 S z=x- ty? a. Describe the direction of the vectors normal to the surface. Choose the correct answer below. O A. The normal vectors point toward the z-axis on the curved surface of S and in the direction of (0, 1,0) on the flat surface of S. O B. The normal vectors point away from the z-axis on the curved surface of S and in the direction of (0, 1, 0) on the flat surface of S. O C. The normal vectors point away from the z-axis on the curved surface of S and in the direction of (0, - 1, 0) on the flat surface of S. O D. The normal vectors point toward the z-axis on the curved surface of S and in the direction of (0, - 1, 0) on the flat surface of S. b. Evaluate J J (VXF) .nds J (XF). nds= (Type an exact answer, using it as needed.) C. Evaluate OF . dr and check for agreement with part (b) . OF . dr = _ (Type an exact answer, using it as needed.)