# The Tetrahedron Problem

Geometry Level 5

$$\vec{a},\vec{b}$$ and $$\vec{c}$$ are three non coplanar unit vectors inclined at an angle $$\alpha (\leq \dfrac{\pi}{2} )$$ to each other . If volume of the tetrahedron formed by these vectors is $$\dfrac{1}{\sqrt{360}}$$. Then find the value of

$3{\cos}^{2} \alpha -2\cos^{3} \alpha.$

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