  This thesis is dedicated to a study of a spin-isospin structure of the
polarized ${}^3\mathrm{He}$. First, an introduction to the spin structure of
${}^3\mathrm{He}$ is given, followed by a brief overview of past experiments.
The main focus of the thesis is the E05-102 experiment at Jefferson Lab, in
which the reactions ${}^3\vec{\mathrm{He}}(\vec{\mathrm{e}},\mathrm{e'}
\mathrm{d})$ and ${}^3\vec{\mathrm{He}}(\vec{\mathrm{e}},\mathrm{e'}
\mathrm{p})$ in the quasi-elastic region were studied. The purpose of this
experiment was to better understand the effects of the S'- and D-state
contributions to the ${}^3\mathrm{He}$ ground-state wave-functions by a precise
measurement of beam-target asymmetries $A_x$ and $A_z$ in the range of recoil
momenta from 0 to about $300 \mathrm{MeV}/c$. The experimental equipment
utilized in these measurements is described, with special attention devoted to
the calibration of the hadron spectrometer, BigBite. Results on the measured
asymmetries are presented, together with first attempts at their comparison to
the state-of-the art Faddeev calculations. The remaining open problems and
challenges for future work are also discussed.
