# Vector calculus

is it true that if $\nabla \cdot \vec{F}=0 , \nabla \times \vec{F}=0$ then $\vec{F}=0$???

robphy
Homework Helper
Gold Member
is it true that if $\nabla \cdot \vec{F}=0 , \nabla \times \vec{F}=0$ then $\vec{F}=0$???
Suppose $$\vec F=3\hat x \ldots$$

the divergence of 3x is 3 not 0 though?

robphy
Homework Helper
Gold Member
the divergence of 3x is 3 not 0 though?
By $$\hat x$$, I mean what you might have seen as $$\hat \imath$$....
that is,
$$\vec F= (3) \hat \imath$$
or
$$\vec F= (3,0,0)$$
...that is, a nonzero constant vector field.