The possibility of a unified description for several weak radiative decays of K mesons is being investigated. In particular, those processes are considered in which the decay mechanism can be related to the strong (or electromagnetic) PVV vertex, namely K+-->e+νγ, K02-->π+π-γ, and K+-->π+γγ, in addition to the process K02-->γγ, which was treated before. Vector gauge fields with current mixing and octet breaking in the PVV vertex are used, as indicated from a phenomenological Lagrangian model fitting the data on strong and radiative meson decays. For the weak nonleptonic interaction we have considered two alternatives, the current-current "simplest" Hamiltonian suggested recently in connection with K02-->γγ decay, as well as the current-current octet Hamiltonian in the form introduced by Sakurai, both satisfying the ΔS=1, ΔI=12 rule. The experimental upper limit on K+-->e+νγ imposes limits on a free parameter of the theory related to the SU(3) symmetry breaking in the PVV vertex. Within these limits we calculate the width for K02-->π+π-γ, which differs considerably from the SU(3)-symmetric value and is predicted to be close to the present experimental upper limit. In the calculation of K+-->π+γγ we consider a new class of diagrams, which appear because of the use of vector gauge fields in the Lagrangian. These diagrams involving four-leg vertices are shown to give the dominant contribution to the decay. The calculated rate and spectrum differ from those of previous calculations.