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Being F a vector field with continous partial derivatives, If rot(F)=0 and Div(F)=0 is F constant?

I tried using Gauss and stokes theorem but i dont see anything

rot(F) = curl(F)?

yep, sry xD here in spanish we call it rot

i think the solution should be find using those theorems

if the curl(F)=0 => F is a conservative vector field

yep, and if Div(F)=0 => F=curl(G) being G another vector field

it's been a while since i've dealt with this stuff so i'm a bit rusty. sorry

@pgpilot326 +1
or its just not actually compressing

and does F is constant mean?
like 1,2,3 ?

yep

well we have an example so that is not true

yep thank you very much guys , i really appreciate the help

or think gravity!
zero curl, zero divergence.

yes and it doesnt have to be necessarily constant, thanks! :)

because that nails it :-)

since:
\[\Large \nabla \times {\mathbf{F}} = {\mathbf{0}}\]

indeed. the curl is zero so can we use the bac cab rule for anything?
like 2 x 0 = 3 x 0
2 = 3

yes! I think so, since the vector equation above, it is an identity

furthermore, also this condition:
\[\Large \nabla \cdot {\mathbf{F}} = 0\]
holds

condition*

thanks!

you need a medal :-)

or 2

lol!

no worries! I'm happy so! thanks! @IrishBoy123

good!