If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}+\hat{k}$, then a vector of magnitude $\sqrt{22}$ which is parallel to $2\vec{a}-\vec{b}+3\vec{c}$ is