You can project P1 (point on ray R1) to the plane defined by R0, giving you P1' and P0' (where the rays intersect that plane)
This gets you the distance between P1 and R0.
Multiply the direction of R1 by that of R0.
Multiply result by the previously mentioned distance.
The resulting point should be the intersection of R0 and R1. So simply check if it lies on R0.
I bet this doesnt work at all.