We study the multifrequency emission and spectral properties of the quasar3C 279 aimed at identifying the radiation processes taking place in the source. Methods: We observed 3C 279 in very-high-energy (VHE, E> 100 GeV) γ-rays, with the MAGIC telescopes during 2011, for the first time in stereoscopic mode. We combined these measurements with observations at other energy bands: in high-energy (HE, E> 100 MeV) γ-rays from Fermi-LAT; in X-rays from RXTE; in the optical from the KVA telescope; and in the radio at 43 GHz, 37 GHz, and 15 GHz from the VLBA, Metsähovi, and OVRO radio telescopes - along with optical polarisation measurements from the KVA and Liverpool telescopes. We examined the corresponding light curves and broadband spectral energy distribution and we compared the multifrequency properties of 3C 279 at the epoch of the MAGIC observations with those inferred from historical observations. Results: During the MAGIC observations (2011 February 8 to April 11) 3C 279 was in a low state in optical, X-ray, and γ-rays. The MAGIC observations did not yield a significant detection. The derived upper limits are in agreement with the extrapolation of the HE γ-ray spectrum, corrected for EBL absorption, from Fermi-LAT. The second part of the MAGIC observations in 2011 was triggered by a high-activity state in the optical and γ-ray bands. During the optical outburst the optical electric vector position angle (EVPA) showed a rotation of ~180°. Unlike previous cases, there was no simultaneous rotation of the 43 GHz radio polarisation angle. No VHE γ-rays were detected by MAGIC, and the derived upper limits suggest the presence of a spectral break or curvature between the Fermi-LAT and MAGIC bands. The combined upper limits are the strongest derived to date for the source at VHE and below the level of the previously detected flux by a factor of ~2. Radiation models that include synchrotron and inverse Compton emissions match the optical to γ-ray data, assuming an emission component inside the broad line region with size R = 1.1 × 1016 cm and magnetic field B = 1.45 G responsible for the high-energy emission, and another one outside the broad line region and the infrared torus (R = 1.5 × 1017 cm and B = 0.8 G) causing the optical and low-energy emission. We also study the optical polarisation in detail and interpret it with a bent trajectory model.