Using the intermediate vector boson (IVB) theory and Cabibbo's SU3 model for the weak interaction, the analytical expressions and numerical results for the differential cross-sections and the longitudinal polarizations of the final state particles of several νN "elastic" reactions have been obtained. The results show that, for the given set of form factors usually assumed, the IVB effects on the longitudinal polarizations of the leptons and the hyperons are substantial near certain outgoing angles when the neutrino energy is high enough. The results also show that some informations about the form factors and the mass of the IVB can be obtained from the experimental results of the differential cross-section and the longitudinal polarization taken together if they are accurate enough. The nuclear effects and the effect of the neutrino beam energy spectrum on the longitudinal polarization of the muon have also been estimated for the process νμ + [ Z, A ] →μ- + [Z + 1, A].