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We study the structural properties like the gravitational mass, radius and tidal deformability of dark matter (DM) admixed strange quark stars (SQSs). For the purpose we consider the vector MIT Bag model to describe the strange quark matter (SQM) and investigate the possible presence of accreted DM in the SQSs consequently forming DM admixed SQSs. We introduce feeble interaction between SQM and the accreted fermionic DM via a vector dark boson mediator. Considering the present literature, in the context of possible presence of DM in SQSs, this work is the first to consider interaction between DM and SQM in the DM admixed SQSs. The mass of the DM fermion ($m_χ$) and the vector mediator ($m_ξ$) and the coupling ($y_ξ$) between them are determined in accordance with the constraint from Bullet cluster and the present day relic abundance, respectively. We find that the presence of DM reduces both the mass and radius of the star compared to the no-DM case. The massive the DM fermion, the lower the values of maximum mass and radius of the DM admixed SQSs. For the chosen values of $m_χ$ and corresponding values of $m_ξ$ and $y_ξ$, the computed structural properties of the DM admixed SQSs satisfy all the various present day astrophysical constraints.We obtain massive DM admixed SQSs configurations consistent with the GW190814 observational data. Hence the secondary compact object associated with this event may be a DM admixed SQS.