If a = i + j + k, b =4 i -2 j +3 k and c = i -2 j + k are three vectors, then a vector of magnitude 6 units, which is parallel to the vector 2 a - b…

If $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}$ and $\displaystyle \vec{c}=\hat{i}-2 \hat{j}+\hat{k}$ are three vectors, then a vector of magnitude $\displaystyle 6$ units, which is parallel to the vector $\displaystyle 2 \vec{a}-\vec{b}+3 \vec{c}$, is