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This thesis is dedicated to a study of a spin-isospin structure of thepolarized ${}^3\mathrm{He}$. 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, inwhich 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 thisexperiment was to better understand the effects of the S'- and D-statecontributions to the ${}^3\mathrm{He}$ ground-state wave-functions by a precisemeasurement of beam-target asymmetries $A_x$ and $A_z$ in the range of recoilmomenta from 0 to about $300 \mathrm{MeV}/c$. The experimental equipmentutilized in these measurements is described, with special attention devoted tothe calibration of the hadron spectrometer, BigBite. Results on the measuredasymmetries are presented, together with first attempts at their comparison tothe state-of-the art Faddeev calculations. The remaining open problems andchallenges for future work are also discussed.

Measurement of double polarized asymmetries in quasi-elastic processes ${}^3\vec{He}(\vec{e},e' d)$ and ${}^3\vec{He}(\vec{e},e' p)$