Statement-1: If the sum of two unit vectors is a unit vector, then the magnitude of their difference is $\sqrt{3}$.

Statement-2: For any two vectors $\vec a$ and $\vec b$ $|\vec a+\vec b|^2+|\vec a -\vec b|^2 = 2\left\{|\vec a|^2+|\vec b|^2\right\}$

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Clearly, statement-2 is true.

Let $\vec a,\vec b$ be two unit vectors such that $\vec a +\vec b$ is a unit vector.

Using statement-2, we have

$1^2+|\vec a-\vec b|^2=2(1+1)⇒|\vec a-\vec b|= \sqrt{3}$

So, statement-1 is true. Also, statement-2 is a correct explanation for statement-1.