Question

A velocity vector is given as $\overrightarrow{v}=5xy\hat{i}+2y^2\hat{j}+3y{z}^2\hat{k}.$ The divergence of this velocity vector at $(1,1,1)$ is

• A. $9$
• B. $10$
• C. $14$
• D. $15$

Answer 1

The correct option is D $15$

Given vector is
$\overrightarrow{v}=5xy\hat{i}+2y^2\hat{j}+3y{z}^2\hat{k}$
$div\overrightarrow{v}=▽.\overrightarrow{v}$
$=\frac{\partial }{\partial x}\left(5xy\right)+\frac{\partial }{\partial y}\left(2y^2\right)+\frac{\partial }{\partial z}\left(3y{z}^2\right)$
$=5y+4y+6yz$
At $(1,1,1)$:
$(div\overrightarrow{V}{)}_{(1,1,1)}=15$