When three coordinates are used, the x, y and z axes are set. These three axes are actually the three directions of three-dimensional space, namely the horizontal axis and the vertical axis. Generally, X is the horizontal axis, Y is the vertical axis, and Z is the vertical axis.

Definition and algorithm

Choose a point O in the space at will, and make the intersection O into three mutually perpendicular number axes Ox, Oy and Oz, all of which take O as the origin and have the same length unit. These three axes are called X axis (horizontal axis), Y axis (vertical axis) and Z axis (vertical axis) respectively, and are collectively referred to as coordinate axes.

Their positive direction conforms to the right-handed rule, that is, the right hand holds the Z axis. When the positive direction of the X axis of the four fingers of the right hand forms an angle with the positive direction of the Y axis, the thumb points to the positive direction of the Z axis. In this way, a spatial rectangular coordinate system is formed, which is called spatial rectangular coordinate system O-xyz. The fixed point o is called the origin of the coordinate system.