We employ the three-dimensional Faddeev equations in the total angular momentum representation to investigate the contributions stemming from the various long-range three-body forces to the low-lying vibrational states of the Ar₃ molecule. The resulting large matrices were handled using the Arnoldi's algorithm and a background potential which can eliminate the plethora of unphysical eigenvalues close to unity. We demonstrated that our method is suited for calculations in relatively heavy trimers without resorting to an explicit partial wave decomposition.