Orientation and rotation in 3D

Working in 3D can sometimes be confusing. You might forget the direction of one of your axes, or what the positive direction of rotation about an axis is.

Here are two simple rules that help you understand relationships in 3D:

The right-hand axes rule

This trick helps you to determine the positive direction of an axis.

Hold your right hand as shown in the figure below. Position your thumb, index finger, and middle finger all at an angle of 90 degree to each other. The middle finger is pointing directly at you.

Your thumb and fingers point to the positive direction of their respective axes.

The right-hand axes rule

As long as you know the direction of two of the axes, you can always determine the direction of the third axis.

The right-hand rotation rule

This trick helps you to determine the positive direction of rotation about any axis.

Hold your right hand as shown in the figure below. Point your thumb in the positive direction of the axis of rotation. Your curled fingers indicate the positive direction of angles measured around the axis.

The right-hand rotation rule