Position and orientation of the end-effector of redundant manipulators perform a core role in various complex tasks. However, most quadratic programming (QP)-based robot control approaches merely take the position of the end-effector into account, which is relatively inadequate and impractical. Driven by this significant deficiency, this article develops a control method for end-effector orientation representations by analyzing a rotation matrix. Specifically, it is formulated as an equality constraint and applied to control issues of Euler angles and axis-angle representation. On this basis, a QP-based position and orientation control (POC) scheme is proposed for the kinematic control of redundant manipulators. To handle such a POC problem, a dynamic neural network (DNN) is designed with rigorous theoretical analyses. Simulation results show that the POC scheme can accurately control the orientation representations and position of the end-effector. Experimental results and comparisons with state-of-the-art approaches highlight the feasibility and superiority of the proposed method.