If \( \vec{a}, \vec{b}, \vec{c} \) are three non-zero vectors and \( \hat{n} \) is a unit vector perpendicular to \( \vec{c} \) such that \( \vec{a}=\alpha \vec{b}-\hat{n} \), \( (\alpha \neq 0) \) and \( \vec{b}\cdot \vec{c}=12 \), then \( \left\lvert \vec{c}\times(\vec{a}\times\vec{b}) \right\rvert \) is equal to:
