Inelastic and quasielastic neutron-scattering measurements have been performed on an amorphous poly(ethylene terephthalate) (PET) fiber in parallel and perpendicular scattering geometries., i.e., when the fiber axis f is parallel and perpendicular to the scattering vector Q, respectively. The so-called boson peak is observed at around -1.4 meV in neutron energy transfer at low temperatures below about 150 K in both the geometries; as temperature increases, the fast process of picosecond order appears at a certain temperature below the glass-transition temperature T-g (= 348 K). Although no drastic differences in the dynamics can be observed, a closer look at the spectra revealed some interesting features of the low-energy modes. From the mean-square displacements evaluated with two different energy resolutions, it was found that the fast process appears only in the direction perpendicular to the polymer chain (not the fiber axis f) in the energy region between -1 and -0.2 meV. In the inelastic scattering spectra, we found that the boson peak is stronger in intensity for the parallel direction while the intensity of the fast process is larger for the perpendicular one. The quantitative analysis based on the recent vibration-relaxation model revealed that the fast process can mainly be explained by the softening of the vibrational modes; the softening occurs at lower temperatures in the perpendicular geometry than in the parallel one. On the other hand, the conventional single-lorentzian fit to the fast process, in which the fast process is assumed to be a relaxational process and described by a Lorentzian, showed that the onset temperature of the fast process is lower in the perpendicular geometry than in the parallel one. These have been tentatively attributed to weaker force constants, for motions perpendicular to a polymer chain, such as torsional and librational motions, than those along the chain.