Cartesian coordinates

Our first task, when dealing with 3-dimensional motion, is to set up a suitable coordinate system. The most straight-forward type of coordinate system is called a Cartesian system, after René Descartes. A Cartesian coordinate system consists of three mutually perpendicular axes, the $x$-, $y$-, and $z$-axes (say). By convention, the orientation of these axes is such that when the index finger, the middle finger, and the thumb of the right-hand are configured so as to be mutually perpendicular, the index finger, the middle finger, and the thumb can be aligned along the $x$-, $y$-, and $z$-axes, respectively. Such a coordinate system is termed right-handed. See Fig. 10. The point of intersection of the three coordinate axes is termed the origin of the coordinate system.

Figure 10: A right-handed Cartesian coordinate system