Perpendiculars to two vectors So this is more than likely a simple question that has been asked before, but if have 2 lines described by the formula:
$V = (x,y,z) + L (i,j,k)$
i.e.  a line described by a position and a length along a unit vector
How would I find the line that is perpendicular to both lines?

A vector perpendicular to both these lines will be perpendicular to their direction vectors, so you need to take the cross (vector) product of their direction vectors. There are going to be an infinite number of (direction) vectors perpendicular to your two lines, so if you want the equation of a perpendicular line you will need also the position vector of a point on that line.
If you don't need this last thing, then you are done with just the cross product!
