Wheeled vehicles are known as systems with non-holonomic constraint, and their trajectory can not be easily controlled using ordinary control strategies. In this paper, we will design a path tracking controller for wheeled vehicles using exact linearization technique and time scale transformation which are developed in nonlinear system theory. In the proposed controller design, we will describe the vehicle's behavior with a nonlinear state equation, whose time scale is the distance along the desired path. Then, we will design a stabilizing controller for this nonlinear state equation using exact linearization technique. We will show, in the simulation, the vehicle with the proposed controller tracks the desired straight line as it is moving forward and/or backward. Based on this path tracking controller, we will also propose the path planning method for parking control of vehicles using forward and backward movement.