How to make an vertex on crossing edges?

[ivla]

As I understand - you need a new vertex on edge exactly in the place where it intersects with another edge.
Here is it.
Warning: orange is a selection color in this examples.

Make a reference oblect:


Select edge that willl be cutted:


Cut it in half (create new vertex):


Click RMB  & select "Intersect [RMB]"


Pick edge to set direction of new vertex movement & click RMB


Pick vertex to move & click RMB


Pick plane on the reference oblect (to which we will move vertex) & click RMB


Pick point on edge that intersects & click RMB


Done.