Find Divergence of Vector Field: $\vec F$

[Reshma]

Given a vector field:

$$\vec F= (x^2-xy)\hat x +(y^2-yz)\hat y +(z^2-xz)\hat z$$

Find the conditon for the divergence to be equal to zero.

 

[da_willem]

How about applying the divergence to this vector field and find out?!

$$\nabla \cdot \vec{v}=\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}+ \frac{\partial v_z}{\partial z}$$

 

[Reshma]

I applied it and got :

$$x+y+z = 0$$

Is that enough or there is more to it?

 

[Doc Al]

That's all there is to it.