Verify that the vector field F = x2 i + (1 - xy) j - xz k is solenoidal, and find a vector potential G for it having the form G(x, y, z) = G1(x, y, z) i + x2y k.
◦ xyz i + x2 y k
◦ (xyz + z) i + x2 y k
◦ (xyz - z) i + x2 y k
◦ (x2y + z) i + x2 y k
◦ (y2z - z) i + x2 y k