📂Mathematical Physics

Notation for Vectors Entering and Exiting the Plane

Definition

As depicted above, from the observer’s perspective, the direction that goes into the plane is denoted as $\otimes$. Conversely, the direction that comes out of the plane is denoted as $\odot$.

Explanation

Looking at the $xy$-plane as shown in the figure above, the $\hat{z}$ direction is $=\odot$ and the $-\hat{z}$ direction is $=\otimes$. This is primarily used in physics, engineering, etc.

The notation is not based on circles and crosses but on the shape of a screw. When there is a wooden plank, if you screw it in from your viewpoint, that direction is going into the plank, and the screw will appear as $\otimes$. If you screw it from the opposite side, the direction will be coming out of the plank, and the screw will appear as $\odot$.