If \(\rm \vec{a}=(2, 1, -1), \vec{b}=(1, -1, 0), \vec{c}=(5, -1, 1),\) then what is the unit vector parallel to \(\rm \vec{a} +\vec{b}-\vec{c}\) in the opposite direction?
1
\(\rm \dfrac{\hat{i}+\hat{j}-2\hat{k}}{3}\)
2
\(\rm \dfrac{\hat{i}-\hat{j}+2\hat{k}}{3}\)
3
\(\rm \dfrac{2\hat{i}-\hat{j}+2\hat{k}}{3}\)
4
None of the above