# Multidimensional Vectors

Geometry Level 3

The angle between the $2015$-dimensional vectors $\vec{a}$ and $\vec{b}$ is $30^{\circ}$. Let $\|\vec{a} \| = \sqrt{8}$ and $\|\vec{b} \| = \sqrt{96}$. Find the value of $\|\vec{a} - \vec{b} \| ^2$.

###### Image Credit: Wikimedia Oleg Alexandrov
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