$\bar{a}, \bar{b}, \bar{c}$ are three non-coplanar and mutually perpendicular vectors of same magnitude $\mathrm{K}. \bar{r}$ is any vector satisfying $\bar{a} \times((\bar{r}-\bar{b}) \times \bar{a})+\bar{b} \times((\bar{r}-\bar{c}) \times \bar{b})+\bar{c} \times((\bar{r}-\bar{a}) \times \bar{c})=\overline{\mathrm{O}}$, then $\bar{r}=$

• Correct answer
  A

  $\frac{\mathrm{K}^2(\bar{a}+\bar{b}+\bar{c})}{3 \mathrm{~K}^2-1}$
• B

  $\frac{\bar{a}+\bar{b}+\bar{c}}{2}$
• C

  $\frac{\mathrm{K}(\bar{a}+\bar{b}+\bar{c})}{\mathrm{K}+1}$
• D

  $\frac{\bar{a}+\bar{b}+\bar{c}}{\mathrm{~K}^2+1}$

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