  Asymmetry measurements were conducted in Jefferson Lab's experimental Hall A
through electron scattering from a polarized $^3$He target in the quasi-elastic
$^3\mathrm{He}(e,e'n)$ reaction. Measurements were made with the target
polarized in the longitudinal direction with respect to the incoming electrons
($A_L$), in a transverse direction that was orthogonal to the beam-line and
parallel to the q-vector ($A_T$), and in a vertical direction that was
orthogonal to both the beam-line and the q-vector ($A_y^0$). The experiment
measured $A_y^0$ at four-momentum transfer squared (Q$^2$) of 0.127
(GeV/$c$)$^2$, 0.456 (GeV/$c$)$^2$, and 0.953 (GeV/$c$)$^2$. The $A_T$ and
$A_L$ asymmetries were both measured at Q$^2$ of 0.505 (GeV/$c$)$^2$ and 0.953
(GeV/$c$)$^2$. This is the first time that three orthogonal asymmetries have
been measured simultaneously. Results from this experiment are compared with
the plane wave impulse approximation (PWIA) and Faddeev calculations. These
results provide important tests of models that use $^3$He as an effective
neutron target and show that the PWIA holds above Q$^2$ of 0.953 (GeV/$c)^2$.
