Plane Vectors

Why

A point in the plane can be interpreted as a displacement.

Definition

A plane vector (or vector, two-dimensional vector, 2-vector) is an element of $\R ^2$. We associate a list of two numbers with a point in the plane, a location. We also associate a list of two numbers with a displacement, a change in location.

Visualization

As in plane geometry, pictures are indispensable (though they are not proofs). In the figure, indicate the vectors $x, y \in \R ^2$ on a plane. We have also indicated the origin, $(0, 0)$, as usual.

Note on terminology

The English word “vector” is from the same Latin word “vector,” meaning, literally, carrier. This sense is from the interpretation of a vector as indicating a displacement.