A model structure of vitreous silica, for which the vibrational frequencies and eigenmodes were calculated from first principles, is used to investigate vibrational amplitudes. Calculated mean-square displacements for oxygen and silicon atoms are obtained as a function of temperature. The square displacement tensors of oxygen atoms show a marked anisotropic character, which is related to the local geometry. The displacements of oxygen atoms along the three principal directions can be associated to distinct parts of the vibrational spectrum, as evidenced by their thermal dependence. These anisotropic effects directly affect the elastic and the static structure factors, which are sensitive to the correlation between displacements of different atoms along their connecting direction. This description shows that the observed widths for Si-O and O-O correlations mainly derive from atomic vibrations rather than from structural disorder. Anisotropic correlations between different atoms are shown to be important up to a distance of 4 Angstrom, i.e., involving atoms that belong to corner-sharing tetrahedra. The scattering functions, calculated at finite temperature and in the harmonic approximation, show good agreement with experiment. In particular, the comparison between the static and the elastic structure factors yields a characterization of the correlated displacements in accord with experimental observations. The static structure factor is significantly affected by anisotropic correlations, but shows only a weak dependence on temperature between 0 and 300 K.