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

$\frac{π}{3}$

Let θ be the angle between unit vectors $\vec a$ and $\vec b$.

Then,

$|\vec a-\vec b|=1$

$⇒|\vec a-\vec b|^2=1$

$⇒|\vec a|^2+|\vec b|^2-2(\vec a.\vec b)=1$

$⇒1+1-2|\vec a||\vec b|\cos θ=1$

$⇒2-2\cos θ=1⇒\cos θ=\frac{1}{2}=θ=\frac{π}{3}$