If a parallelogram is constructed on the vectors $\vec{a} = 3\vec{p} - \vec{q}$ and $\vec{b} = \vec{p} + 3\vec{q}$, where $|\vec{p}| = 3$, $|\vec{q}| = 2$ and the angle between $\vec{p}$ and $\vec{q}$ is $\pi/3$, then the ratio of the lengths of adjacent sides $|\vec{a}|$ and $|\vec{b}|$ of the parallelogram is:

• A
  $\sqrt{57} : \sqrt{52}$
• B
  $\sqrt{67} : \sqrt{63}$
• C
  $\sqrt{63} : \sqrt{47}$
• D
  $\sqrt{57} : \sqrt{54}$