To find the points of intersection of a line that is perpendicular to two skew lines.

So given two SKEW lines (in Euclidian space) finding the shortest distance between them is fine, but how would you find the points of intersection of the two lines with the line of shortest distance (i.e. the line that is mutually perpendicular to both skew lines)?

E.g. given L1: r= (2+m)i + (3+2m)j + (4+2m)k

and L2: r= (3+f)i + (3+ f)j + (4+3f)k

(where f and m are parameters)

I believe they are skew, now how to find the line that passes through L1 and L2 and is mutually perpendicular to both? I can find the direction vector (by crossing the two other vectors) but I need a known point...

Help very appreciated!!! thanks!!!