2. Consider two spheres of equations x+ y+z = 2x-2y+4z-2 and x + y+z=4x+2y+4. (a) For which points P on the first sphere and Q on the second sphere is the distance d(P,Q) maximum? (b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight his V = Th (3R - h).) 3. Find an equation for the surface obtained by rotating (a) the ellipse x2 +4y = 4, z = 0, about the x-axis (b) the hyperbola x - y = 1, z=0, about the y-axis (c) the line y=4z, x = 0 about the z-axis. Specify the name of each of the obtained surface. 4. (a) Find an equation and then identify the surface that consists of all points P which are equidistant from(-1, 0, 0) to the plane x = 1.