$\bar{a}=\bar{i}+\bar{j}-2 \bar{k}, \bar{b}=\bar{i}+2 \bar{j}-3 \bar{k}, \bar{c}=2 \bar{i}-\bar{j}+\bar{k}$ are three vectors. If $\bar{r}$ is a vector such that $\overline{\mathrm{r}} \cdot \overline{\mathrm{a}}=0, \overline{\mathrm{r}} \cdot \overline{\mathrm{c}}=3$ and $[\overline{\mathrm{r}} \overline{\mathrm{a}} \overline{\mathrm{b}}]=0$, then $|\overline{\mathrm{r}}|=$

• Correct answer
  A

  $\sqrt{2}$
• B

  $\sqrt{3}$
• C

  $3$
• D

  $7$

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