Does anybody know how to intersect two perpendicular lines?

The sketch (3D-sketch) below are made as an example. Line A is fixed to the origin. Line B hover a bit above line A. The two lines are not in any other way constrained to reference geometry. Therefore I can't see any way to use relations such as "Along X", "Normal", "Vertical" etc.

My purpose: I will use lines (or any other geometry) from two pipes or components, which I want to be perpendicular to each other but at the same time meet at the center.

You mean like this?