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