If \(\vec{a}, \vec{b}, \vec{c}\) are three non-zero vectors and \(\hat{n}\) is a unit vector perpendicular to \(\vec{c}\…

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 \(|\vec{c} \times(\vec{a} \times \vec{b})|\) is equal to:

[JEE Main 2023, 30 Jan (Shift 1)]