Let \( \vec{a}=4\hat{i}-\hat{j}+\hat{k} \) and \( \vec{b}=11\hat{i}-\hat{j}-\hat{k} \) and \( \vec{c} \) be a vector such that \( (\vec{a}+\vec{b})\times\vec{c}=\vec{c}\times(2\vec{a}+3\vec{b}) \). If \( (2\vec{a}+3\vec{b}).\\vec{c}=1670 \), then \( |\vec{c}|^2 \) is equal to:
