The resultant of two vectors $\overrightarrow{\mathrm{P}}\text{ and }\overrightarrow{\mathrm{Q}}\text{ is }\overrightarrow{\mathrm{R}}\text{.}$  What happen to the new resultant vector is perpendicular to $\overrightarrow{\mathrm{P}}\cdot \overrightarrow{\mathrm{R}},\text{ when }\overrightarrow{\mathrm{Q}}$ is doubled.

• A

  $\left(\frac{{\mathrm{P}}^2-{\mathrm{Q}}^2}{2\mathrm{PQ}}\right)$

• B

  Q

• C

  $\frac{P}{Q}$

• D

  $\frac{\mathrm{p}+\mathrm{Q}}{\mathrm{p}-\mathrm{Q}}$