Question
If $ \vec{a} $ and $ \vec{b} $ are unit vectors, then what is the angle between $ \vec{a} $ and $ \vec{b} $ for $ \sqrt{3} \, \vec{a} \cdot \vec{b} $ to be a unit vector?
If $ \vec{a} $ and $ \vec{b} $ are unit vectors, then what is the angle between $ \vec{a} $ and $ \vec{b} $ for $ \sqrt{3} \, \vec{a} \cdot \vec{b} $ to be a unit vector?