Context: The determination of the magnetic field vector in quiescent solar prominences is possible by interpreting the Hanle and Zeeman effects in spectral lines. However, observational measurements are scarce and lack high spatial resolution. Aims: To determine the magnetic field vector configuration along a quiescent solar prominence by interpreting spectropolarimetric measurements in the He I 1083.0 nm triplet obtained with the Tenerife Infrared Polarimeter installed at the German Vacuum Tower Telescope of the Observatorio del Teide. Methods. The He I 1083.0 nm triplet Stokes profiles are analyzed with an inversion code that takes into account the physics responsible of the polarization signals in this triplet. The results are put into a solar context with the help of extreme ultraviolet observations taken with the Solar Dynamic Observatory and the Solar Terrestrial Relations Observatory satellites. Results: For the most probable magnetic field vector configuration, the analysis depicts a mean field strength of 7 gauss. We do not find local variations in the field strength except that the field is, in average, lower in the prominence body than in the prominence feet, where the field strength reaches 25 gauss. The averaged magnetic field inclination with respect to the local vertical is 77 degrees. The acute angle of the magnetic field vector with the prominence main axis is 24 degrees for the sinistral chirality case and 58 degrees for the dextral chirality. These inferences are in rough agreement with previous results obtained from the analysis of data acquired with lower spatial resolutions.