Let \(\rm \vec{a}=\hat{j}-\hat{k}\) and \(\rm \vec{c}= \hat{i}-\hat{j}-\hat{k}\). Then the vector \(\rm \vec{b}\) satisfying \(\rm (\vec{a}\times \vec{b})+\vec{c}=0\) and \(\rm \vec{a}\cdot \vec{b}=3\), is
1
\(\rm - \hat{i}+\hat{j}-2\hat{k}\)
2
\(\rm 2\hat{i}-\hat{j}+2\hat{k}\)
3
\(\rm \hat{i}-\hat{j}-2\hat{k}\)
4
\(\rm \hat{i}+\hat{j}-2\hat{k}\)