946. Find the divergence of the vector field:
1) $\bar{r}=x i+y \bar{j}+z k$
2) $\bar{p}=\frac{\bar{i}+\bar{i}+\bar{k}}{\sqrt[3]{(x+y+z)^{2}}}$
3) $\vec{q}=e^{x y}(y \bar{j}-x \bar{i}+x y \bar{k})$.
Solution. Applying formula (2):

1) $\operatorname{div} \dddot{r}(M)=\frac{\partial r_{x}}{\partial x}+\frac{\partial^{r} y}{\partial y}+\frac{\partial r_{z}}{\partial z}=1+1+1=3$.
2) $p_{x}=p_{y}=p_{z}=(x+y+z)^{-\frac{2}{3}}$;

$$
\frac{\partial \rho_{x}}{\partial x}=\frac{\partial \rho_{y}}{\partial y}=\frac{\partial \rho_{z}}{\partial z}=-\frac{2}{3 \sqrt[3]{(x+y+2)^{6}}}
$$

$\operatorname{div} \bar{p}(M)=-2(x+y+z)^{-\frac{5}{3}}=f(M)$
3) $q_{x}=-x e^{x y} ; q_{y}=y e^{x y} ; q_{z}=x y e^{x y}$; $\frac{\partial q_{x}}{\partial x}=-e^{x y}(1+x y)=-\frac{\partial q_{y}}{\partial y} ; \quad \frac{\partial q_{z}}{\partial z}=0 ; \operatorname{div} \eta(M)=0$.

The obtained results have the following meaning: