Zero divergence

[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.