A reduced dimensionality (RD) reactive quantum scattering model has been presented for the general type AB+XCD(3)reversible arrow ABX+CD3 reaction, where the CD3 fragment has C-3V symmetry. The model Hamiltonian and quantum scattering formulas are derived in hyperspherical coordinates, together with a single hyperradius hyperspherical projection method for boundary conditions. The time-independent coupled channel equations are propagated using a log-derivative method. The surface functions are produced by a guided spectral transform (GST) Lanczos algorithm. We also describe a GST Lanczos method to solve the generalized eigenvalue problem in a nonorthogonal basis. The RD model has been applied to the OH+CH(4)reversible arrowH(2)O+CH3 reaction. A comparison of calculated results with previous theoretical and experimental ones is made. (C) 2001 American Institute of Physics.