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 \(\hat{b} \) ?

120°

$|\hat a+\hat b|=1⇒|\hat a+\hat b|^2=(\hat{a}+\hat{a}).(\hat{b}+\hat{b})=1$

\(\hat{a}.\hat{a} + \hat{b}.\hat{b} + 2\hat{a}.\hat{b} = 1\)

$1 + 1 + 2\hat{a}.\hat{b} = 1$  

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

\(-\frac{1}{2}\) = \(\cos {\theta}\)

\(\theta = 120°\)