orthogonality
Orthogonality is the careful, all-dimensions word for perpendicular. Two vectors are orthogonal exactly when their dot product is zero. In the plane that means they meet at a clean right angle, like the corner of a sheet of paper.
Why care? Orthogonal directions carry independent, non-overlapping information. A push purely east tells you nothing about how far north you went. So if your reference directions are orthogonal, you can adjust one without disturbing the others.
This is the quiet foundation of every tidy coordinate system. The x, y, and z axes are mutually orthogonal, which is exactly why reading off a point's coordinates is so painless.
Dot product zero means the two vectors meet at a right angle.
By convention the zero vector is orthogonal to everything, since its dot product with anything is zero.