Vector Algebra

Let \(\vec{a}=3 \hat{i}+2 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{c}\) be a vector such that \((\vec{a}+\vec{b}) \times \vec{c}=2(\vec{a} \times \vec{b})+24 \hat{j}-6 \hat{k}\) and \((\vec{a}-\vec{b}+\hat{i}) \cdot \vec{c}=-3\). Then \(|\vec{c}|^2\) is equal to ________.