  The new vector resonance $X_1(2900)$ observed recently by LHCb in the $
D^{-}K^{+}$ invariant mass distribution in the decay $B^{+} \to
D^{+}D^{-}K^{+}$ 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 $u^{T}C\gamma_5d$ and heavy antidiquark $\overline{c}
\gamma_{\mu}\gamma_5C\overline{s}^{T}$. 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 $X_1 \to D^{-}K^{+}$
and $X_1 \to \overline{D}^{0}K^{0}$. The strong couplings $g_1$ and $g_2$
corresponding to the vertices $X_1D^{-}K^{+}$ and $X_1\overline{D} ^{0}K^{0}$
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 $X_1(2900)$ $m=(2890~\pm 122)~\mathrm{MeV}$, and for its full width
$\Gamma _{\mathrm{full}}=(93\pm 13)~\mathrm{MeV}$ 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^{+} \to D^{+}D^{-}K^{+}$
may reveal doubly charged four-quark structures $
[uc][\overline{s}\overline{d}]$.
