\( \mathbf{F}(x, y)=\left(x y+y^{3}\right) \mathbf{i}+\left(x^{4}+3 x y\right) \mathbf{j} \)
Added by Angela W.
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The vector-valued function $$ \mathbf{F}(x, y)=y \mathbf{i}+x^{2} \mathbf{j}+x y \mathbf{k} $$ is an example of a vector field in the $x y$ -plane.
Topics In Vector Calculus
Vector Fields
$\mathbf{F}(x, y)=\frac{x \mathbf{i}+y \mathbf{j}}{\sqrt{x^{2}+y^{2}}} .$ [Note: Each vector in the field is a unit vector in the same direction as the position vector $\mathbf{r}=x \mathbf{i}+y \mathbf{j} .$ ]
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