Q:

Algorithm for detection of overlaping between vectors

I am currently developing a math-physics program and I need to calculate if two vectors overlap one another, the one is vertical and the other is horizontral.  Is there any fast algorithm to do this because what I came up so far, has a lot of repeats.  Eg lets say we have vector V1((0,1),(2,1)) and a V2((1,0),(1,2)) where the first parenthesis is the coordinates starting and the second coordinates that the vector reaches.  I want as a result to take that they overlap at (1,1)
So far the only idea I came up is to ''expand'' each vector to a list of points and then compare the lists e.g for V1 its list would be (0,1) (1,1) (2,1)

A:

If you have two line segments and you want to know if they intersect, see https://en.wikipedia.org/wiki/Line_intersection and https://en.wikipedia.org/wiki/Line_segment_intersection. 
For next time, I'd expect you to do more research on your own.   See especially "computational geometry", e.g., a textbook that covers that area.