Two vectors $\overline{\mathrm{P}}$ and $\overline{\mathrm{Q}}$ are magnitudes $(\mathrm{A}+\mathrm{B})$ and $(\mathrm{A}-\mathrm{B})$ acting at a point produce a resultant of magnitude $\sqrt{3{\mathrm{A}}^2+{\mathrm{B}}^2}$.
Statement I: Angle between vectors $\overline{\mathrm{P}}$ and $\overline{\mathrm{Q}}$ is 120°.
Statement II: If angle between vectors $\overline{\mathrm{P}}$ and $\overline{\mathrm{Q}}$ is doubled then the square of the resultant is ${\mathrm{A}}^2+3{\mathrm{B}}^2$.