An electric dipole (discussed in detail in Section 4.7) consists of two point charges of equal and opposite magnitude ±Q spaced by distance d. With the charges along the z axis at positions z = ±d/2 (with the positive charge at the positive z location), the electric field in spherical coordinates is given by E(r, θ) = [Qd/(4π0r³)][2 cos θa_r + sin θa_θ], where r >> d. Using rectangular coordinates, determine expressions for the vector force on a point charge of magnitude q (a) at (0, 0, z); (b) at (0, y, 0).