Question

The divergence of the vector field $\overrightarrow{A}=x{\hat{a}}_x+y{\hat{a}}_y+z{\hat{a}}_z$ is

• A. $0$
• B. $1/3$
• C. $1$
• D. $3$

Answer 1

The correct option is D $3$

$\overrightarrow{A}=x{\hat{a}}_x+y{\hat{a}}_y+z{\hat{a}}_z$
$div\overrightarrow{A}=▽.\overrightarrow{A}$
$=(\hat{i}\frac{\partial }{\partial x}+\hat{j}\frac{\partial }{\partial y}+\hat{k}\frac{\partial }{\partial z}).(x{\hat{a}}_x+y{\hat{a}}_y+z{\hat{a}}_z)$
$=1+1+1=3$