Let a, b, c be three non-coplanar vectors such that a × b =4 c, b × c =9 a and c × a =α b, α>0. If | a |+| b |+| c |=1/36, then α is equal to \ \ \ \.

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