Let \( \vec{a}=\hat{i}+2\hat{j}+\hat{k} \), \( \vec{b}=3(\hat{i}-\hat{j}+\hat{k}) \). Let \( \vec{c} \) be the vector such that \( \vec{a}\times\vec{c}=\vec{b} \) and \( \vec{a}\cdot\vec{c}=3 \). Then \( \vec{a}\cdot\left((\vec{c}\times\vec{b})-\vec{b}-\vec{c}\right) \) is equal to:
