Question 2 We have given a surface S, similar to a cylinder (the discs at the top and bottom are included) with the center along the z-axis, radius r = 7, bottom in the xy-plane and height h = 7 (peak in z =7) x+3 F y + 3 In this problem we will calculate the flux of the vector field out of the cylinder. Since we work with a cylinder, it is natural to use cylinder coordinates x = r cos(0), y = rsin(0), z = z (r = x2 + y2, 0 E [0, 2x]) With cylinder coordinates, the vector field will be given as 7 . cos(0) + 3 F = 7 . sin(0) + 3 We want the cylinder to be oriented outwards. The orientation of the cylinder can be described by the orientation of each side surface. Let /"1 be the orientation of the top surface, N"2be the orientation of the bottom surface and /"3 be the orientation of the side surface. What do these orientations look like? The answer must be in Cartesian coordinates, where each component is a function of r, 0 and z. Type "theta" instead of 0. Hint: Only N* 3depends on which point (x, y, z) you are looking at. N1 = N 2 = N3 =