If $\vec a$ and $\vec b$ are two unit vectors such that $\vec a + \vec b$ is also a unit vector, then find the angle between $\vec a$ and $\vec b$ is

120°

Since $\vec a$ and $\vec b$ are unit vectors, $(\vec a+\vec b) . (\vec a+\vec b) = 1$

$⇒ \vec a.\vec a+\vec b.\vec b+2\vec a.\vec b=1$

$⇒1+1+ 2\vec a.\vec b=1⇒\vec a.\vec b= -1/2$

Hence the angle θ between $\vec a$ and $\vec b$ is given by 

$cosθ = -1/2⇒ θ =120°$

Hence (D) is the correct answer.