Chapter 14 - Vector Calculus - 14.1 Vector Fields - 14.1 Exercises - Page 1057: 2

The sketch for $F=\langle x,y\rangle$ is given below,

Let $x$ and $y$ be defined on a region $R$ of $ℝ$. A vector field in $ℝ^2$ is a function $F$ that assigns to each point in $R$ a vector. Which is given below, $F=\langle x,y\rangle$ A vector field $F=\langle x,y\rangle$ is continuous or differentiable on a region $R$ of $ℝ^2$ if $x$ and $y$ are continuous or differentiable on $R$,respectively. The sketch for $F=\langle x,y\rangle$ is given below,