Axis–angle representation

Imagine a toy car that can move in any direction. The car has a steering wheel that can turn it around in different directions. The direction the car is facing is called the "axis" and the amount of turning that the steering wheel does is called the "angle". In the same way, the axis-angle representation is a way to describe the orientation of an object in space.

The "axis" in this case is a straight line that runs through the center of the object. It is kind of like the steering wheel of the toy car. The "angle" is the amount that the object is rotated around this axis. It is kind of like how much you turn the steering wheel of the toy car.

So, if you want to describe the orientation of an object using the axis-angle representation, you need to say: (1) what the axis is and (2) how much the object is rotated around that axis.

For example, let's say you have a pencil that is standing upright on a table. The axis of the pencil is the line that runs through the center of the pencil from top to bottom. Now let's say you rotate the pencil by 45 degrees around this axis. This means the pencil is still standing upright on the table, but it is now pointing in a different direction. So the axis-angle representation of this orientation would be: the axis is the line running through the center of the pencil from top to bottom, and the angle is 45 degrees.