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
Answer & explanation
Correct answer: option 2
Let θ be the angle between unit vectors $\vec a$ and $\vec b$.
Then,
$|\vec a-\vec b|=1$
$⇒|\vec a-\vec b|^2=1$
$⇒|\vec a|^2+|\vec b|^2-2(\vec a.\vec b)=1$
$⇒1+1-2|\vec a||\vec b|\cos θ=1$
$⇒2-2\cos θ=1⇒\cos θ=\frac{1}{2}=θ=\frac{π}{3}$