Let \( \vec{a},\vec{b},\vec{c} \) be three non-coplanar vectors such that \( \vec{a}\times \vec{b}=4\vec{c},\, \vec{b}\times \vec{c}=9\vec{a} \) and \( \vec{c}\times \vec{a}=\alpha \vec{b} \) and \( \alpha>0 \). If \( |\vec{a}|+|\vec{b}|+|\vec{c}|=\dfrac{1}{36} \), then \( \alpha \) is equal to ________.
