If a, b, c are three non-zero vectors and n is a unit vector perpendicular to c such that a =α b - n,(α ≠ 0) and b · c =12, then | c ×( a × b )| is…

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