The vector-dominance-model (VDM) relation between the reactions (a) πp→ρΔ and (b) πp→ωΔ and the reaction (c) γp→πΔ is investigated within the context of the Regge-pole model. Parameters for the strong-interaction processes are determined by making a least-squares fit to the differential cross section and spin-density-matrix data. We find that good agreement with the experimental measurements can be obtained by including the π, A1, and A2 trajectories for reaction (a), while for reaction (b) we need the exchange of the ρ and B trajectories. Using values of the photon-vector-meson coupling constants, as determined from the leptonic decays of these mesons, and the VDM relations between the amplitudes for processes (a)-(c), we calculate the differential cross section for reaction (c). This is found to be in good agreement with the experimental data and yields a χ2=3 for nine data.