In this work, the vectorial formalism previously developed [Gatti , J. Chem. Phys. 108, 8804 (1998); 108, 8821 (1998)] is extended to radial coordinates and to the general study of dimers. This method is general and avoids the direct use of differential calculus in the derivation of the kinetic operator. Moreover, to study the spectrum of NH3, an exact and simple kinetic energy operator is proposed. The new system of coordinates (a combination of Jacobi and hyperspherical coordinates) fully displays the permutation symmetry of the three hydrogen atoms. It is adapted to study the umbrella motion and furthermore minimizes the Coriolis terms.