Does anybody know how to solve this problem?

Given the 3 direction vectors emanating from one apex(P0, at the origin),
d1,d2,d3,
and the corresponding lengths of the sides of the opposite face s12, s13, s23,
solve
the tetrahedron. A solution consists of either:
the plane equation of the opposite face (P1,P2,P3)
the coordinates of either P1, P2, or P3
the distance from P0 to any other apex

For a graphical version of the problem statement, email pbierre@...