How do you find the intersection of 2 lines in space?

Answer 1

By solving simultaneous linear equations.

(If you don't know how to do this, it's a bit more complicated than can be detailed here, but basically you cast the equations for the two lines into the form

ax + by = z

and then see if there are any valid solutions to the equation a1x + b1y = a2x + b2y. If so, that's your answer. If not, the lines are skew and do not intersect.)