/sci/ - Science & Math

Assume we have 2 pairs of arbitrary line segments in 3d space. Each segment is described by a point and a vector, point + vector * 1 = end of segment, point + vector * 0 = start of segment. I'm looking for a way to find points where:
p = seg1(a) + (seg2(a) - seg1(a)) * c
and
p = seg3(b) + (seg4(b) - seg3(b)) * d
Where a,b,c and d are [0 1].
In other words the points must be both on a line between a point a certain percentage along segment 1's length and the same same percentage along segment 2's length, and the same must apply for a seperate percentage between segment 3 and 4. Anyone know how I could go about solving this, or whether it's even solveable?