JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 30

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 $\left|\vec a\right|+\left|\vec b\right|+\left|\vec c\right|=\dfrac1{36}$, then $\alpha$ is equal to ______.