Let the vectors \( \vec{a}=-\hat{i}+\hat{j}+3\hat{k} \) and \( \vec{b}=\hat{i}+3\hat{j}+\hat{k} \). For some \( \lambda,\mu\in \mathbb{R} \), let \( \vec{c}=\lambda \vec{a}+\mu \vec{b} \). If \( \vec{c}\cdot(3\hat{i}-6\hat{j}+2\hat{k})=10 \) and \( \vec{c}\cdot(\hat{i}+\hat{j}+\hat{k})=-2 \), then \( |\vec{c}|^2 \) is equal to:
