Vector Algebra

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