  We investigate how galaxy pairs are oriented in three dimensions within
cosmic filaments using data from the EAGLE simulation. We identify filament
spines using DisPerSE and isolate galaxies residing in filamentary
environments. Employing a FoF algorithm, we delineate individual filaments and
determine their axes by diagonalizing the moment of inertia tensor. The
orientations of galaxy pairs relative to the axis of their host filament are
analyzed. Our study covers diverse subsets of filaments identified through
varying linking lengths, examining how galaxy pairs align with the filament
axis across different spatial parameters such as pair separation and distance
from the filament spine. We consistently observe a strong alignment pattern
characterized by the probability distribution for the cosine of the orientation
angle, which is nearly identical in each case. Furthermore, the study
investigates the impact of redshift space distortions, confirming that the
alignment signal persists in both real and redshift space. To validate our
method, we employ Monte Carlo simulations with different theoretical
probability distributions. Our results reaffirm previous findings with
projected two-dimensional distributions and extend our understanding of how
filaments impact the spatial organization and evolution of galaxies across
cosmic scales.
