Question

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

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 :).