Definition:Vector/Affine Geometry

Definition
Let $\mathcal E$ be an affine space.

Let $V$ be the tangent space of $\mathcal E$.

Any element $v$ of $V$ is called a vector.

Notation
If $p, q \in \mathcal E$ are points then it is common to write $\vec{pq} = q - p \in V$.

Also see

 * Definition:Vector