Let $\vec{a}=\hat{i}-\hat{j},\vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times \vec{c}+\vec{b}=0$ and $\vec{a}.\vec{c}=4$ then ${\left|\vec{c}\right|}^2$ is equal to :-