The vector sum of two vectors \( \vec{P} \) and \( \vec{Q} \) is \(...

The vector sum of two vectors \( \vec{P} \) and \( \vec{Q} \) is \( \vec{R} \). If vector \( \vec{Q} \) is reversed, the resultant becomes \( \vec{S} \). Then, prove that
\[
\mathrm{R}^{2}+\mathrm{S}^{2}=2\left(\mathrm{P}^{2}+\mathrm{Q}^{2}\right)
\]