Think carefully about the definition of angular momentum, as shown in this file ans
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I have to point out that one must know the position vector if one wants to determine angular momentum, because angular momentum depends on the relative position.
The only situation where the angular momentum doesn’t depend on the reference point is when the two linear momentum are exactly opposite of each other, i.e., they have the same magnitude and opposite direction (only opposite directions do not suffice). In this case, we may simplify the result to be d*p where d is the distance and p is the momentum of one of the particle.
For a general situation, if there is no r1, r2, there is simply no solution to this question.
