After spending some time researching ray tracing implementation and solving simultaneous equations, I had the feeling there should be vector formulation to this problem. Anyway since I'm not a mathematician I wasn't going to easily happen upon the answer by myself. As it happens The vector form of the solution did exist and I was able to find it at the following links.

The Math Forum : Vector Algebra - Finding the Intersection Point

Math Stack Exchange : Find intersection of two 3D lines

As this work is related to a broader set of tools I'm developing, the code is implemented in python. Although the same could be done in VEX or VOPS.