Let \(\hat{a}\) and \(\hat{b} \) be two unit vectors such that \(\hat{a} + \hat{b} \) is also a unit vector. Then what is the angle \(\hat{a}\) and \(\hat{b} \) ?

30° 60° 90° 120°

120°

\(\hat{a}.\hat{a} + \hat{b}.\hat{b} + 2\hat{a}.\hat{b} = 1\) 1 + 1 + 2\(\hat{a}.\hat{b}\) = 1   \(\hat{a}.\hat{b}\) = \(-\frac{1}{2}\) = \(\cos {\theta}\) \(-\frac{1}{2}\) = \(\cos {\theta}\) \(\theta = 120°\)