The lines obviously are parallel (the direction vectors are scalar multiples), so there is a plane that contains them. There are lots of ways to find the equation of that plane, but if you have technology at hand, the fastest way is probably to solve a system created by the points you can get out of your lines:

A(1) + B(2) + C(-3) + D = 0 (L1, k=0)

A(-3) + B(1) + C(5) + D = 0 (L1, k=1)

A(-11) + B(-1) + C(21) + D = 0 (L2, L=0)

A(-3) + B(1) + C(5) + D = 0 (L2, L=1)