Let a = i +2 j +3 k, b =3 i + j - k and c be three vectors such that c is coplanar with a and b. If the vector c is perpendicular to b and a · c =5,…

Let $\displaystyle \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=3 \hat{i}+\hat{j}-\hat{k}$ and $\displaystyle \vec{c}$ be three vectors such that $\displaystyle \vec{c}$ is coplanar with $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$. If the vector $\displaystyle \vec{c}$ is perpendicular to $\displaystyle \vec{b}$ and $\displaystyle \vec{a} \cdot \vec{c}=5$, then $\displaystyle |\vec{c}|$ is equal to