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 \( \|\vec{a} - \vec{b} \| ^2 \).