If $\vec{a}=(2,1,-1), \vec{b}=(1,-1,0), \vec{c}=(5,-1,1)$, then wha is the unit vector parallel to $\vec{a}+\vec{b}-\vec{c}$ in the opposite direction?

• A

  $\frac{\hat{i}+\hat{j}-2 \hat{k}}{3}$
• B

  $\frac{\hat{i}-2 \hat{j}+2 \hat{k}}{3}$
• Correct answer
  C

  $\frac{2 \hat{i}-\hat{j}+2 \hat{k}}{3}$
• D

  None of the above

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