Find a vector function r(u,v)for the surface.

a. The plane that passes through the point (1,2,3) and is parallel to the vectors1,1,1 and1,1,1.

b. The lower half of the ellipsoid 2x²+4y²+z²=1

c. The part of the sphere of radius 4 centered at the origin that lies between the planes z =2 and z = 2