Question

The divergence of the vector field $(x-y)\hat{i}+(y-x)\hat{j}+(x+y+z)\hat{k}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

Let $r=(x-y)\hat{i}+(y-x)\hat{j}+(x+y+z)\hat{k}$
$div.\overrightarrow{r}=\frac{\partial }{\partial x}(x-y)+\frac{\partial }{\partial y}(y-x)+\frac{\partial }{\partial z}(x+y+z)$
$=1+1+1=3$