Find a field $F$ in the xy-plane with the property that at each point $(x, y) \not = (0, 0)$, $F$ is a unit vector pointing away from the origin. The field is undefined at $(0, 0)$.
I understand that a unit vector is a vector $\dfrac{\overrightarrow{v}}{|\overrightarrow{v}|}$ such that it has the direction of $\overrightarrow{v}$ but magnitude of $1$. I also understand that a vector field is a function that assigns a vector to each point in its domain.
However, I have no idea how to approach such a problem. I would greatly appreciate it if people could please take the time to teach me how to solve such a problem. I would like to gain an understanding of the reasoning involved in each step of solving such a problem.