perpendicularity vectors, unit vector

Hello

So i have 3 curves (red, green and blue) every curve is made od 117 (x,y,z) cordinates. Then i have unit vector for each point on blue curve (cosalpha, cosbeta, cosgama). I need to get the distance betwen the curves using the unit vector. So i made a lot of line representing unit vector (length of vector is unknown). And then i tried to perpendicularity vectors from red/green curve to unit vectors and then using Pythagorean theorem to get the distance. I have no clue how to do it. Im glad for any advice.

[Torsten]

Brute-force method:

Check which of the 117x117 combinations of points yields the smallest value for distance.

[Dominik Cech]

Yeah, I already did this.

But what I wanted is this. The blue cylinder has axis same as the unit vector and i would like to know in which point it interferace with the green/red curve and from that point i want to know distance betwen them. Like in the first picture I conected first point with first point etc. But becouse of the unit vectros there might be that i need to conect 10th point on green/red with 26th point on blue curve.