If ${\bf r}=(x,y,z)$ and $r=||{\bf r} || $does $\nabla . {\bf r} =0$?

Question

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If ${\bf r}=(x,y,z)$ and $r=||{\bf r} || $is $\nabla . {\bf r} =0$ ?

In terms of derivatives of fields I know that $\nabla . r$ I'm aware it should give a scalar. But I'm unsure if it gives $0$ or $1$

I have attached the question as I don't know how to use mathsjax

Answer 1

you simply carry out the operation of $\nabla$ on the vector ${\bf r}=(x,y,z)$ you get: $\nabla\cdot{\bf r}=3$, $\nabla{ r}={\bf r}/r$, $\nabla\times {\bf r}={\bf 0}$