Let a = i +2 j +3 k and b = i + j - k. If c is a vector such that a · c =11, b ·( a × c )=27 and b · c =-√ 3 | b |, then | a × c |^2 is equal to ____.

Let $\displaystyle \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}$ and $\displaystyle \vec{b}=\hat{i}+\hat{j}-\hat{k}$. If $\displaystyle \vec{c}$ is a vector such that $\displaystyle \vec{a} \cdot \vec{c}=11$, $\displaystyle \vec{b} \cdot(\vec{a} \times \vec{c})=27$ and $\displaystyle \vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|$, then $\displaystyle |\vec{a} \times \vec{c}|^2$ is equal to $\displaystyle \_\_\_\_$.