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 $\|\vec{a} - \vec{b} \| ^2$ .

Multidimensional Vectors

Image Credit: Wikimedia Oleg Alexandrov