We have studied the quasielastic {sup 3}He(e,e{sup '}p){sup 2}H reaction in perpendicular coplanar kinematics, with the energy and the momentum transferred by the electron fixed at 840 MeV and 1502 MeV/c, respectively. The {sup 3}He(e,e{sup '}p){sup 2}H cross section was measured for missing momenta up to 1000 MeV/c, while the A{sub TL} asymmetry was extracted for missing momenta up to 660 MeV/c. For missing momenta up to 150 MeV/c, the cross section is described by variational calculations using modern {sup 3}He wave functions. For missing momenta from 150 to 750 MeV/c, strong final-state interaction effects are observed. Near 1000 MeV/c, the experimental cross section is more than an order of magnitude larger than predicted by available theories. The A{sub TL} asymmetry displays characteristic features of broken factorization with a structure that is similar to that generated by available models.