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 \( \alpha \in \left[0,\dfrac{\pi}{3}\right] \) 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:
