Consider three vectors a, b, c. Let | a |=2,| b |=3 and a = b × c. If α ∈[0, (π)/3] is the angle between the vectors b and c, then the minimum value…

Consider three vectors $\displaystyle \vec{a}, \vec{b}, \vec{c}$. Let $\displaystyle |\vec{a}|=2,|\vec{b}|=3$ and $\displaystyle \vec{a}=\vec{b} \times \vec{c}$. If $\displaystyle \alpha \in\left[0, \frac{\pi}{3}\right]$ is the angle between the vectors $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$, then the minimum value of $\displaystyle 27|\vec{c}-\vec{a}|^2$ is equal to: