An amplitude analysis of Λc+→pK-π+ decays together with a measurement of the Λc+ polarization vector in semiōleptonic beauty hadron decays is presented. A sample of 400 000 candidates is selected from proton-proton collisions recorded by the LHCb detector at a center-of-mass energy of 13 TeV. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. The mass and width of the Λ(2000) state are also determined. A significant Λc+ polarization is found. A large sensitivity of the Λc+→pK-π+ decay to the polarization is seen, making the amplitude model suitable for Λc+ polarization measurements in other systems.