proving a common perpendicular intersects the two skew lines

hi there,

i have been trying to figure out this problem all week!!! please can someone help?

PROBLEM:
L1 and L2 are skew lines. suppose A and B are points on L1 and L2 respectively and that u and v are vectors parallel to L1 and L2 respectively. show that there exist points P and Q on L1 and L2 respectively such that PQ is perpendicular to both L1 and L2.

i assume you'd do it using parametric equations so i have:
L1: p = a + t_1u
L2: q = b + t_2v

PQ = (b-a) + t_2v - t_1u

uXv is perpendicular to both L1 and L2 so it would be in that direction.

after this i am stuck...?

thanks so much for any help guys!