I'm sure this question has been asked before. However, I'm trying to connect the dots by translating an equation on paper into an actual function. I thought It would be interesting to ask here instead on the Math sites (since it's going to be used for games anyway ).

Let's say we have our vector equation :

 x = s + Lr;

where x is the resulting vector, s our starting point/vector. L our parameter and r our direction vector.

The ( not sure it's called like this, please correct me ) normal equation is :

x.n = c;

If we substitute our vector equation we get:

(s+Lr).n = c.

We now need to isolate L which results in

L = (c - s.n) / (r.n);

L needs to be 0 < L < 1. Meaning it needs to be between 0 and 1.

My question: I want to know what L is so if I were to substitute L for both vector equation (or two lines) they should give me the same intersection coordinates. That is if they intersect.

But I can't wrap my head around on how to use this for two lines and find the parameter that fits the intersection point. Could someone with a simple example show how I could translate this to a function/method?