Vector field with parallel field lines

Question

If the field lines of vector field $\mathbf{F}(x,y)$ are parallel, what can be said about the divergence and curl of the field? I think the curl must be zero but divergence can get value.

Answer 1

Analyze these vector fields to discover what can happen:

${\bf F_1}(x,y)=(y,0)$

${\bf F_2}(x,y)=(x,0)$

${\bf F_3}(x,y)=(xy,0)$

${\bf F_4}(x,y)=(1,0)$