Rectangular cartesian co-ordinate system:

In classical mechanics, it is considered that there are three dimensions in space. These three dimensions are represented by three axes in the cartesian co-ordinate system. These three axes are X-axis, Y-axis and Z-axis, which are mutually perpendicular to each other. The origin is denoted by the fixed point where these three axes meet. A point in this space is represented by the three co-ordinates (x,y,z). Three co-ordinates x, y and z epresents the distance of the point from the origin along the X-axis, Y-axis and Z-axis respectively.

There are two types of co-ordinate systems:

• (i) Right-handed co-ordinate system,
• (ii) Left-handed co-ordinate system.

(i) Right-handed co-ordinate system:

There are three axes in the right-handed co-ordinate system. These three axes are taken in such a way that, if a right-handed screw is rotated in the anti-clockwise direction through a small angle from X-axis to Y-axis, then the screw will move forward in the direction of the positive Z-axis.

The representation of the right-handed cartesian co-ordinate system is shown in the adjoining Fig.1. Here X-axis and Y-axis are taken in the plane of the paper, and Z-axis is perpendicular to the plane of the paper, Z-axis is pointing upward.

On the other hand, if we stretch the middle finger, thumb and first finger of right hand mutually at right angle to each other, now, if the midle finger and the thumb represen along the X-axis and Y-axis respectively, then the first finger will represent along the Z-axis.

(ii) Left-handed co-ordinate system:

The mirror reflection of the right-handed system represents the Left-handed system., i.e., it can be obtained by changing the direction of one of the co-ordinate axes of the right-handed system as shown in the adjoining Fig. 2. The three axes are taken in such a way that, when the head of a left-handed screw is rotated through a small angle from X-axis to Y-axis then the screw will move forward in the direction of the Z-axis.

Here X-axis and Y-axis are taken in the plane of the paper, and Z-axis is perpendicular to the plane of the paper and the Z-axis is pointing upward.

On the other hand, if we stretch the thumb, 1st finger and midle finger in such a way that they all are mutually perpendicular to each other, then the 1st finger will point along the Z-axis when the middle finger and the thumb point along the X-axis and Z-axis respectively.