The pH of 0.001 M $C{H}_{3}COOH$ is

pH = $-log\left[H^{+}\right]$ = -log[0.001] = 3.

But, $C{H}_{3}COOH$ is a weak acid which dissociates partially & it has $K_a$ value < 1.

$C{H}_{3}COO{H}_{\left(aq\right)}\rightleftharpoons C{H}_{3}CO{O}_{\left(aq\right)}^{-}+H_{\left(aq\right)}^{+}$

 For most of the acid pH value is always less than 7.

Hence, the correct option is option 3) Between 3 and 7.