How do I find the equation of a line that passes through point and two skew lines

Question

This is not an orthogonal line cutting through two skew lines at a shortest possible distance. This is just some line cutting those skew lines at some angle and also going through a point.

Skew line 1 =

x = 2l - 7

y = 3l - 14

z = l

Skew line 2 =

x = 3m - 10

y = 2m - 6

z = m

Point (1,2,0).

Thanks a lot in advance. I want to understand how this works :).

Answer 1

The line has to lie both in the plane spanned by the point and the first line and the plane spanned by the point and the second line, so one option is to find the result by intersecting these two planes.