Question

Divergence of the vector field
$V(x,y,z)=-(xcosxy+y)\overline{i}+\left(ycosxy\right)\overline{j}+(sin{z}^2+x^2+y^2)\overline{k}$ is

• A. $2zcos{z}^2$
• B. $sinxy+2zcos{z}^2$
• C. $xsinxy-cosz$
• D. none of thesse

Answer 1

The correct option is A $2zcos{z}^2$

Ans : (a)

$V\left(x,y,z\right)=-(x\cos xy+y)i+\left(y\cos xy\right)j+\left[sin\right(z^2)+(x^2)+(y^2\left)\right]k$
Divergence .$V$
$=\frac{\partial V_x}{\partial x}+\frac{\partial V_y}{\partial y}+\frac{\partial V_z}{\partial Z}$
$=-cosxy+x\left(sinxy\right)y+cosxy-ysin\left(xy\right)x+2zcos{z}^2$
$=2zcos{z}^2$