Question
If $ \vec{a} $, $ \vec{b} $, and $ \vec{c} $ are unit vectors satisfying $ |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 = 9 $, then find the value of $ |2\vec{a} + 5\vec{b} + 5\vec{c}| $.
If $ \vec{a} $, $ \vec{b} $, and $ \vec{c} $ are unit vectors satisfying $ |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 = 9 $, then find the value of $ |2\vec{a} + 5\vec{b} + 5\vec{c}| $.