How to make an vertex on crossing edges?

[lennart]

I guess that it moves a vertex to intersect of plane, not edge

UPD: It can be done in a more simple way.

Pick vertex to move (on target object)
Intersect [LMB]
Pick edge to set direction (on target object)
Pick plane to intersect (on reference object)

Yeah, thanks, this worked. Tried also some different options to learn the program.

@ Micheus: both objects are contacting.