Thankyou again for taking your time to reply to my question.

I am having real difficulties in implementing this. Please if you could spend a moment on this simple problem and tell me where I'm going wrong? Say I have these two simple line segments:

Line segment 1 defined by points a( -6, 0, 0 ), and b( 4, 0, 0 ) and
Line segment 2 defined by points c( -1, -5, 0 ), and d( -1, 5, 0 ) with the origin o( 0, 0, 0 ).

The line segments would look something like this (slightly offset from the origin):

c
|
|
a------o---b
|
|
d

The point of intersection should be ( -1, 0, 0 ).

So from here I build an equation for each of the dimensions. What would these equations look like? I am doing something wrong.

Once I have the equations and they are re-arranged I should be able to use just two of the equations in a gaussian elimination to find the point of intersection? Or am I just finding the point along the lines where they do intersect (the number between 0 and 1) and I have to work from that (a whole other problem)? What would a gaussian elimination give me in this situation, the point or the [0,1] values?

Please if you could just explain where I am going wrong with my interpretation and what these equations might look like given the example.

Your help and time is appreciated much, thankyou so much.