\begin{document}$ B \rightarrow (V\rightarrow \pi^{+}\pi^{-})P $\end{document} is investigated using the perturbative QCD (PQCD) method, where P represents a pseudoscalar meson, and V refers to ρ, ω, and ϕ mesons. We present the amplitude of the quasi-two-body decay process and investigate the effects of mixed resonances involving \begin{document}$ \rho^{0}-\omega $\end{document}, \begin{document}$ \rho^{0}-\phi $\end{document}, and \begin{document}$ \omega-\phi $\end{document} while considering the impact of isospin symmetry breaking. We observe significant CP asymmetry when the invariant mass of the \begin{document}$ \pi^{+}\pi^{-} $\end{document} pair is within the resonance ranges of ρ, ω, and ϕ mesons. Consequently, we quantify the regional CP asymmetry in these resonance regions. A significant difference is observed when comparing the results obtained with and without the interference of the three vector mesons and isospin conservation. The CP asymmetry results obtained from the three-body decay process, without interference owing to isospin conservation by the PQCD method, are in agreement with the newly updated data acquired by the LHCb experiment."> CP asymmetry from the effect of isospin symmetry breaking during <i>B-</i>meson decay -
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