what are i, j, k? Are those the unit vectors?
The perpendicular distance is the minimum distance, yes.
You can compute that by taking a plane that contains L1 and is parallel to L2. The distance of B to that plane is the perpendicular distance.
If you want to compute the exact points P and Q, you can tage the general Points of L1 and L2, compute the vector between them, and then solve the system of linear equations where that difference is perpendicular to both L1 and L2.