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 $\vec b$ $|\vec a+\vec b|^2+|\vec a -\vec b|^2 = 2\left\{|\vec a|^2+|\vec b|^2\right\}$
Answer & explanation
Correct answer: option 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.