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 $$\vec{c} \times \vec{a} = \alpha\vec{b}$$, $$\alpha > 0$$. If $$|\vec{a}| + |\vec{b}| + |\vec{c}| = {36}$$, then $$\alpha$$ is equal to _______.