$\vec{a}$ and $\vec{b}$ are unit vectors and $\lvert \vec{a} + \vec{b} \rvert = 1$. What is the angle between them?

Explanation

1. 01

   $\lvert \vec{a} + \vec{b} \rvert^{2} = 1 + 1 + 2\cos \theta = 1$.

2. 02

   $\cos \theta = -\frac{1}{2}$, so $\theta = \frac{2\pi}{3}$.