Question

The divergence of vector $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$ is

• A. $\hat{i}+\hat{j}+\hat{k}$
• B. $3$
• C. $0$
• D. $1$

Answer 1

The correct option is B $3$

$\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$
Divergence is
$▽.\overrightarrow{r}=(\frac{\partial }{\partial x}\hat{i}+\frac{\partial }{\partial y}\hat{j}+\frac{\partial }{\partial z}\hat{k}).(x\hat{i}+y\hat{j}+z\hat{k})$
$=1+1+1=3$