\begin{equation} \textnormal{Let } B \textnormal{ be a set in } \mathbb{R}^2. \textnormal{ A vector field on } \mathbb{R}^2 \textnormal{ is a function } \textbf{F} \textnormal{ that assigns to each point (x, y) in } B \textnormal{ a two-dimensional vector } \textbf{F}(x,y). \qquad (\textnormal{Definition of a 2D vector field}) \end{equation}