Displacement Vector: A vector that represents the change in position from one point to another. It is given by $\Delta \mathbf{r} = \mathbf{r}_f - \mathbf{r}_i$ where $\mathbf{r}_f$ and $\mathbf{r}_i$ are the final and initial position vectors.
Velocity Vector: A vector that represents the rate of change of displacement with respect to time. It is defined as $\mathbf{v} = \frac{d\mathbf{r}}{dt}$.
Cartesian Coordinates: A coordinate system that specifies each point uniquely by a set of numerical coordinates, which are the signed distances from the point to two or three fixed perpendicular directed lines, measured in the same unit of length.