As you might have noticed, there are different ways to position the axes. However, there is a convention to draw the axes. The following rules can be used in deciding on the directions of the axes.
Fig 2.4
Fig 2.5
The cork will move up when turned in an anticlockwise direction. Similarly, starting from x-direction and moving in the y-direction (anticlockwise), the z - direction will be the direction of the cork, that is upward.
On the contrary, in the following example, the z axis will point downwards.
Fig 2.6
Fig 2.7
Taking the grip from x to y (that is anticlockwise direction), the thumb gives the direction of the z axis.
Fig 2.8