  Recently, it has been reported the discovery of a dense ring around the
trans-Neptunian object 50000 Quaoar. The ring particles seem to be very close
to the 6/1 mean motion resonance with Weywot, the only known satellite in the
system. In this work we investigate the dynamical environment in the close
vicinity of the 6/1 orbital resonance in the context of the restricted three
body problem. We aim to analyze whether, in view of observational constraints,
the ring could be effectively evolving in resonant motion with the satellite.
Through the technique of dynamical maps we identify and characterize the 6/1
mean motion resonance, finding that the main location of the resonance deviates
by only $29$ km from the central part of the ring. This difference lies within
the 3$\sigma$ confidence level, considering the uncertainties in the
observational parameters. We also show that the Weywot's eccentricity plays a
significant role in the dynamical structure of the 6/1 resonance. The results
show that the resonance width is smaller than the estimated ring's width. Under
assumption of a ring with eccentricity smaller than 0.05, clumping of test
particles appears at the position of the different resonant multiplets,
considering the nominal value of Weywot's eccentricity. This is in agreement
with observations, which indicate that the estimated resonance width ($\leq$ 10
km) is comparable with the narrow and dense arc of material within Quaoar's
ring. Our results may be an indicative that the 6/1 resonance resonance plays a
key role in confining the arc ring.
