If $\bar{p}, \bar{q}, \bar{r}$ are three mutually perpendicular vectors of equal magnitude and if a vector $\bar{x}$ satisfies the equation $\bar{p} \times((\bar{x}-\bar{q}) \times \bar{p})+\bar{q} \times((\bar{x}-\bar{r}) \times \bar{q})+\bar{r} \times((\bar{x}-\bar{p}) \times \bar{r})=\bar{o}$ then $\bar{x}$ is

• A

  $\frac{1}{4}(\bar{p}-\bar{q}+\bar{r})$
• B

  $\frac{2}{3}(\bar{p}+\bar{q}-\bar{r})$
• C

  $\frac{3}{4}(\bar{p}+2 \bar{q}+\bar{r})$
• Correct answer
  D

  $\frac{1}{2}(\bar{p}+\bar{q}+\bar{r})$

Hence, the correct answer is option: 'D'.