Problem 2. (max. 30210+10+10 points) Consider the surface .91 in R3 given by the parametrisation ,3(u, c) = {ucos(c), usin(1:), 41L 112), O Q \"Ll. SQ 6, D a: \"L! Q 2K. (1) (a) Let P0 he the point (1, 0, 3) on the surface 31. Give a normal-point equation for the tangent plane T1581 to 81 at the point B]. (b) Compute the surface integral ffF-dS, where F($1y,z) = (:r,y, 43), and where '91 31 should be oriented upwards (that is, the normal vectors should have a positive 2- component). (c) Suppose a particle is moving along the grid curve of the surface .91 that we get when we set 1! = D in (1), from the origin 0 to the point A = (6, 0, 12), and then it is moving along a circle of radius 6 in the plane a = 12 going from point A to point B = (0, 5, 12) and then to point C = (6, D, 12), and nally returns to the origin from point C along the grid curve that we get when setting 'L-' 2 ET in (1) (see gures below}. What is the total work done by the vector eld G = (D, :r, $) on the particle