In this paper we present a numerical quantum mechanical study for vibrational predissociation on a single electronic potential surface of a T-shaped van der Waals molecule X ⋯ |CB where X is a rare-gas atom while BC is a conventional diatomic molecule. The rare-gas atom is constrained to move on a line perpendicular to the interatomic axis of the BC molecule. The interaction between X and atoms B and C is represented by a sum of Morse atom-atom potentials. The close-coupling scattering equations were solved numerically and the vibrational predissociation rates were related to the widths of the resulting resonances. The method is applied to the HeI 2 (B) van der Waals complex. We also present numerical results for the vibrational relaxation of linear X⋯B-C molecules where the three atoms are restricted to move on a single line. Good correspondence with the approximate (distorted wave) analytical results previously derived by us for ArI2, NeI2, and HeI2 is obtained.