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Given that $\vec a,\vec b.\vec p$ and  $\vec q$ are four vectors such that $\vec a + \vec b = \mu \vec p$, $\vec b.\vec q = 0$ and ${\left( {\vec b} \right)^2}=1$ then $\left| {\left( {\vec a.\vec q} \right)\vec p - \left( {\vec p.\vec q} \right)\vec a} \right|$ is equal to

• A
  $2\left| {\vec p.\vec q} \right|$
• B
  $\frac{1}{2}\left| {\vec p.\vec q} \right|$
• C
  $\left| {\vec p \times \vec q} \right|$
• ✓
  $\left| {\vec p.\vec q} \right|$