Question

Divergence of the vector field $x^{2}z\hat{i}+xy\hat{j}-y{z}^2\hat{k}$ at $(1,-1,1)$ is

• A. 0
• B. 3
• C. 5
• D. 6

Answer 1

The correct option is C 5

$▽.\overrightarrow{F}=\frac{\partial F_1}{\partial x}+\frac{\partial F_2}{\partial y}+\frac{\partial F_3}{\partial z}$
$=2xz+x-2yz$
at $(1,-1,1):▽.\overrightarrow{F}=2\times 1\times 1+1-(2\times -1\times 1)$
$▽.\overrightarrow{F}=5$