The optimal trajectory-tracking control of a Tri-TiltRotor Unmanned Aerial Vehicle is the subject of this paper. This specific UAV design possesses the capability to control the orientation of its main rotors, thus enabling operation in both the Vertical Take-Off and Landing as well as the Fixed-Wing flight mode configuration. The translational controller developed is based on a Linear-Quadratic tracking scheme. Additionally to the proposed controller, the newly introduced capability for rotor-tilting, and thus thrust vectoring, as provided by this design is proposed for its utilization in the control of the longitudinal degree-of-freedom of the UAV. Simulation and experimental results are presented, demonstrating both the overall proposed controller's efficiency, as well as the clear advantage gained by the aforementioned proposed strategy, with regard to the controlled system's longitudinal control performance.