If three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfy $\vec{a}+\vec{b}+\vec{c}=\vec{0}$, then angle between $\vec{a}$ and $\vec{b}$ is:

$\frac{2 \pi}{3}$

$\vec{a}+\vec{b}=-\vec{c}$

$\Rightarrow|\vec{a}+\vec{b}|^2=|\vec{c}|^2=1$

$\Rightarrow|\vec{a}|^2+|\vec{b}|^2+2 \vec{a} . \vec{b}=1$

$\Rightarrow \vec{a} . \vec{b}=-\frac{1}{2}$

$\Rightarrow|\vec{a} \| \vec{b}| \cos \theta=-\frac{1}{2}$

$\Rightarrow \cos \theta=-\frac{1}{2}$

$\Rightarrow \theta=-\frac{2 \pi}{3}$

Hence (2) is correct answer.