5. Consider an ellipsoid which centers at the coordinate origin and has semi-principal axes a, b, C, respectively. In terms of the Cartesian coordinates, its surface is described by the equation 2 2 2 x y z _ E+E+E'L @ (a) (I point) Parametrize the surface of the ellipsoid using two angular variables 9 and qt, in a way that is analogous to the polar angle and the azimuthal angle in the spherical coordinate system. Explicitly write down the parametric form for x, y and z in terms of 6 and 45:. (b) (1 point) Consider Green's theorem applied to any vector eld v: f(V-v)dr=v-da, (3) (v S where 'V is the interior of the ellipsoid and S is the surface of the ellipsoid. Express the area element vector da in terms of the parameters 6 and qt. Find the Cartesian components of da. (0) (1 point) Calculate the volume of the ellipsoid by choosing a convenient vector eld v and then applying Green's theorem Eq. (3)