A)If the two lines are different and parallel they never intesect according to euclid Axioms.
hence we should take that the lines L1 and L2 are different ,non parallel and intersect.
i.e L1
L2
let us assume that there exists two planes P1 and P2 such that the lines L1 and L2
both lie in P1 and P2.
now L1 is in P1 and P2 ,And L2 is in P1 and P2 .
since the L1 lies in both the planes ,we can say that P1 intersects P2 in a straight line(say L)
But if two planes intersect each other then the intersection must be aunique straight line.
Hence L=L1
similarly L=L2
=>L1=L2 which is absurd.
Hence there does not exist another plane P2 to the given conditions in the problem.
B)
Let L1 and L2 are parallel to each other.
To arrive at some contradiction ,we suppose that the planes constituted by L1 and L2 are different. (say P1 and P2)
then L1 contained in both P1 and P2,similarly L2 contained in P1 and P2.
i.e P1 and P2 intersect in two diffrent straight lines and also they are parallel.
But this ia a contradiction to the fact that Two planes intersect in a unique straight line only .
Hence we must've P1=P2.
Hence the the plane derived from the two parallel lines is unique.
END