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 $|\vec{c}|^2$ is equal to :

(1) $19\over2$

(2) $8$

(3) $17\over2$

(4) $9$

(1) $19\over2$

(2) $8$

(3) $17\over2$

(4) $9$