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Multivariable Calculus

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Divergence of General Radial Vector Field

MVCALC-KLVWXZ

Let $\vec{r}=(x,y,z)$ be a radial vector field in $\mathbb{R}^3$, $p$ is a real number, the rescaled vector field:

$$\vec{F}=\frac{\vec{r}}{\|\vec{r}\|^p}$$

...is also a radial vector field, the divergence of $\vec{F}$ is

A

$\text{div }\vec{F}=\frac{3-p}{\|\vec{r}\|^p}$

B

$\text{div }\vec{F}=\frac{3-p}{\|\vec{r}\|^2}$

C

$\text{div }\vec{F}=\frac{1}{\|\vec{r}\|^p}$

D

$\text{div }\vec{F}=\frac{p-3}{\|\vec{r}\|^3}$

E

$\text{div }\vec{F}=0$