The new vector resonance X-1 (2900) observed recently by LHCb in the D-K+ invariant mass distribution in the decay B+ -> D+ D- K+ is studied to uncover internal structure of this state, and calculate its physical parameters. In the present paper, the resonance X-1(2900) is modeled as an exotic vector state, J(P) = 1(-), built of the light diquark u(T)C gamma(5)d and heavy antidiquark (c) over bar gamma mu gamma C-5 (s) over bar (T). The mass and current coupling of X-1(2900) are computed using the QCD two-point sum rule approach by taking into account various vacuum condensates up to dimension 10. The width of the resonance X-1(2900) is saturated by two decay channels X-1 -> D- K+ and X-1 -> (D) over bar K-0(0). The strong couplings g(1) and g(2) corresponding to the vertices X1D- K+ and X-1(D) over bar K-0(0) are evaluated in the context of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. Results for the mass of the resonance X-1(2900) m = (2890 122) MeV, and for its full width Gamma(full) = (93 +/- 13) MeV are smaller than their experimental values reported by the LHCb collaboration. Nevertheless, by taking into account theoretical and experimental errors of investigations, interpretation of the state X-1 (2900) as the vector tetraquark does not contradict to the LHCb data. We also point out that analysis of the invariant mass distribution D+ K+ in the same decay B+ -> D+ D- K+ may reveal doubly charged four-quark structures [uc][(s) over bar(d) over bar]. (C) 2021 Elsevier B.V. All rights reserved.