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An amplitude analysis of the Ξ c+ → pK−π+ decay together with a measurement of the Ξ c+ polarization vector in semileptonic beauty-hadron decays is presented. The analysis is performed using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb − 1 . An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. A sizeable Ξ c+ polarization is found. A large sensitivity of the Ξ c+ → pK−π+ decay to the polarization is seen, making the amplitude model suitable for Ξ c+ polarization measurements in other systems.