The lines EF and GH I have obtained both have the direction vector:

(L - a)/2 i + (m-b)/2 j + n/2 k

This implies that the two lines are parallel/ There is no unique intersection point.
How do I show that these two lines do intersect?

I have tried typing my working using Microsoft word but the formatting was affected when I pasted it here. What is the best way of typing maths on this forum?

Any help would be much appreciated!