Answer
FALSE
Work Step by Step
Given: curl $\mathbf{F}=xi+yj+zk$
Every vector function $\mathbf{F}$ satisfies the property div (curl $\mathbf{F})= 0$
div curl $\mathbf{F}=div (xi+yj+zk) $
div curl $\mathbf{F}=\frac{∂ (x)}{∂x}+\frac{∂ (y)}{∂y}+\frac{∂ (z)}{∂z} $
div curl $\mathbf{F}=1+1+1 = 3 $
Hence, div (curl $\mathbf{F})\ne 0$
$\mathbf{F}$ cannot exist because div curl $\mathbf{F}$ = 3.
