A search for the production of a heavy B quark, having electric charge -1/3 and vector couplings to W, Z, and H bosons, is carried out using proton-proton collision data recorded at the CERN LHC by the CMS experiment, corresponding to an integrated luminosity of 19.7  fb−1. The B quark is assumed to be pair produced and to decay in one of three ways: to tW, bZ, or bH. The search is carried out in final states with one, two, and more than two charged leptons, as well as in fully hadronic final states. Each of the channels in the exclusive final-state topologies is designed to be sensitive to specific combinations of the B quark-antiquark pair decays. The observed event yields are found to be consistent with the standard model expectations in all the final states studied. A statistical combination of these results is performed, and upper limits are set on the cross section of the strongly produced B quark-antiquark pairs as a function of the B quark mass. Lower limits on the B quark mass between 740 and 900 GeV are set at a 95% confidence level, depending on the values of the branching fractions of the B quark to tW, bZ, and bH. Overall, these limits are the most stringent to date.