Question

The divergence of the vector field $3xz\hat{i}+2xy\hat{j}-y{z}^2\hat{k}$ at a point $(1,1,1)$ is equal to

• A. $7$
• B. $4$
• C. $3$
• D. $0$

Answer 1

The correct option is C $3$

Let $\overrightarrow{A}=3xz\hat{i}+2xy\hat{j}-y{z}^2\hat{k}$
$▽.\overrightarrow{A}=\frac{\partial }{\partial x}\left(3xz\right)+\frac{\partial }{\partial y}\left(2xy\right)+\frac{\partial }{\partial z}(-y{z}^2)$
$=3z+2x-2yz$
Divergence at $(1,1,1)$
$▽.\overrightarrow{A}=3$