Vector Algebra: JEE Main 2022 Mathematics question

Let $\overrightarrow a$, $\overrightarrow b$, $\overrightarrow c$ be three non-coplanar vectors such that $\overrightarrow a$ $\times$ $\overrightarrow b$ = 4$\overrightarrow c$, $\overrightarrow b$ $\times$ $\overrightarrow c$ = 9$\overrightarrow a$ and $\overrightarrow c$ $\times$ $\overrightarrow a$ = $\alpha$$\overrightarrow b$, $\alpha$ > 0. If $\left| {\overrightarrow a } \right| + \left| {\overrightarrow b } \right| + \left| {\overrightarrow c } \right| = {1 \over {36}}$, then $\alpha$ is equal to __________.