7. This problem discusses general rotation vector fields. (a) (3 points) A general rotation vector field is given by Fa = a x r where a = (a1, a2, a3) is a constant and r = (x, y, z) is the radial vector field. Make a sketch showing the axis of rotation for a = (1, -1, 1) and little arrows showing how the vector field rotates around the axis. (b) (2 points) Find the general rotational vector field with axis of rotation a = (1, -1, 1). (c) (1 point) Compute the curl of the vector field Fa. Think about the direction this vector points and compare it to the torque. (d) (8 points) Sketch the top half of the hemisphere z = v1 -x2 -y2, and some normal vectors for it. Sketch the axis of rotation of your vector field, as well as a few vectors showing the curl. Think about "projecting" the curl onto each of those normal vectors you sketched. Compute both sides of Stokes' Theorem for the rotation vector field found above and this hemisphere