This study aims to address the issues of the simultaneous control of the angle of attack, sideslip angle, and airspeed of a flight in a vectorial form. A vector controller, with a symmetry structure, is developed to transform the attitude and speed control problem into a space-vector tracking problem. We first establish flight vector-coupled dynamics, i.e., describe velocity and angular-velocity vectors in a body-fixed frame, and then propose a multivariable backstepping sliding mode control algorithm along with nonlinear disturbance observers for the vectorial dynamics. The theoretical analysis ensures that the states of the system can be enforced to reach a small neighborhood of the desired sliding manifold. The results of the numerical simulation illustrate the effectiveness and robustness of the combined vector-control scheme.