If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{r}$ is a non-zero vector such that $p\vec{r} + (\vec{r} \cdot \vec{b})\vec{a} = \vec{c}$,then $\vec{r} = $

• A
  $\frac{\vec{c}}{p} - \left( \frac{\vec{b} \cdot \vec{c}}{p^2} \right)\vec{a}$
• B
  $\frac{\vec{a}}{p} - \left( \frac{\vec{c} \cdot \vec{a}}{p^2} \right)\vec{b}$
• C
  $\frac{\vec{b}}{p} - \left( \frac{\vec{a} \cdot \vec{c}}{p^2} \right)\vec{c}$
• D
  $\frac{\vec{c}}{p^2} - \left( \frac{\vec{b} \cdot \vec{c}}{p} \right)\vec{a}$