you said that one of the methods would be to find the two other direction vectors...
to find a direction vector you would need a point, do we pick any x and y value solve for z and thats a point.. (a, b, c) then direction vector is (x-a, y-b, c-z).
then use dot produt to solve for x, y z?
then do the same thing agian?
and its probably not a coincidence.. we may have been useing the same text book... it is after all, a small world