If the difference of two unit vectors is again a unit vector, then th…

The correct answer is Option (3) → 60°

Let 'a' and 'b' be two unit vectors.

$|a|=1,|b|=1$

and,

$|a-b|=1$

also,

$|a-b|=\sqrt{|a|^2+|b|^2-2|a||b|\cos θ}$

$1=2-2\cos θ$

$⇒\cos θ=\frac{1}{2}$

$⇒θ=\cos^{-1}(\frac{1}{2})=60°$