Let \( \vec{a},\vec{b},\vec{c} \) be three vectors such that \( |\vec{a}|=\sqrt{31},\;4\;|\vec{b}|=|\vec{c}|=2 \) and \( 2(\vec{a}\times\vec{b})=3(\vec{c}\times\vec{a}) \). If the angle between \( \vec{b} \) and \( \vec{c} \) is \( \dfrac{2\pi}{3} \), then \( \left(\dfrac{\vec{a}\times\vec{c}}{\vec{a}\cdot\vec{b}}\right)^{2} \) is equal to ______.
