I confess that I can’t get it:
Vectors are directions (you can think of them as “rays” originated from Plane.WorldXY.Origin: kinda the rays from a light source).
If you “apply” a vector to, say, a point (i.e. p+/-v) then the point is moved “along” that direction. Same with some Translate trans related with a given geometry etc etc. With these in mind … the term vector intersection has no meaning (but a vector angle [with respect a given plane] and/or Dot/Cross products have).
If you have 2 pts (p1, p2) and 2 vectors(v1,v2) then you can have 2 lines. Then there’s various Methods for finding min/max distance using finite or not segments.