$\hat{i}-2 \hat{j}+\hat{k}, 2 \hat{i}+\hat{j}-\hat{k}, \hat{i}-\hat{j}-2 \hat{k}$ are the position vectors of the vertices $A, B, C$ of a triangle $A B C$ respectively. If $D$ and $E$ are the mid points of $B C$ and $C A$ respectively, then the unit vector along $\overrightarrow{D E}$ is

• A

  $\frac{1}{7}(3 \hat{i}-2 \hat{j}+6 \hat{k})$
• Correct answer
  B

  $\frac{1}{\sqrt{14}}(-\hat{i}-3 \hat{j}+2 \hat{k})$
• C

  $\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}-\hat{k})$
• D

  $\frac{1}{13}(12 \hat{i}+3 \hat{j}+4 \hat{k})$

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