I have a couple of lines described by InfiniteLine and I need points where two different pairs of them intersect:

velAnormal[t_] = InfiniteLine[pointA, velocityAvector[pointA, t][[1]]] velBnormal[t_] = InfiniteLine[pointB, Cross[velocityBvector[t]]] velCnormal[t_] = InfiniteLine[pointC, velocityAvector[pointC, t][[1]]] P1[t_] := RegionIntersection[velBnormal[t], velCnormal[t]] P2[t_] := RegionIntersection[velBnormal[t], velAnormal[t]] 

Both P1 and P2 give a Point[x,y] with coordinates, but only within certain operations: @@, Delete[#,0] /@ P1[t] or Delete[0] /@ P1[t] and maybe some other suggestions I found online all display error messages related to RegionIntersection, but attempting to use P1[t] or even P1[0] in a formula results a Point[] with the coordinates. How do I get coordinates and coordinates only?