Assuming a gravitational origin for the Fe iiiλλ2039-2113 redshift and using microlensing based estimates of the size of the region emitting this feature, we obtain individual measurements of the virial factor, f, in 10 quasars. The average values for the Balmer lines, $\langle {f}_{{\rm{H}}\beta }\rangle =0.43\pm 0.20$ and $\langle {f}_{{\rm{H}}\alpha }\rangle =0.50\pm 0.24$ , are in good agreement with the results of previous studies for objects with lines of comparable widths. In the case of Mg ii, consistent results, ${f}_{\mathrm{Mg}{\rm{II}}}\sim 0.44$ , can be also obtained accepting a reasonable scaling for the size of the emitting region. The modeling of the cumulative histograms of individual measurements, CDF(f), indicates a relatively high value for the ratio between isotropic and cylindrical motions, $a\sim 0.4\mbox{--}0.7$ . On the contrary, we find very large values of the virial factor associated to the Fe iiiλλ2039-2113 blend, ${f}_{\mathrm{Fe}{\rm{III}}}=14.3\pm 2.4$ , which can be explained if this feature arises from a flattened nearly face-on structure, similar to the accretion disk.