Radial vector field
= Radial vector field
{title2=$\mathbf F(\mathbf r)=f(r)\mathbf r$}
A <vector field> directed along the radius from a fixed origin, with magnitude depending only on radius. In three-dimensional Euclidean space and away from the origin, $\mathbf F=f(r)\mathbf r=rf(r)\hat{\mathbf r}$. The <product rule> gives $\nabla\cdot\mathbf F=3f+rf'$, and the <curl> vanishes because the derivative matrix is symmetric. These identities alone do not establish regularity at the origin.