For two vectors A and B, $|A+B|=|A-B|$ is always true when a) $$ |A|=|B| \neq 0 $$ b) $$ A \perp B $$ c) $|A|=|B| \neq 0 \quad$ and $A$ and $B$ are parallel or antiparallel d) when either $|A|$ or $|B|$ is zero

Answer: The correct option is a) & d)

Given in question $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$, it can be assertive when $| A |=0$ or $| B |=0$ or both are zero.
The provided statement can also be true if both requirements are met at the same time, which is what is meant by

|A|=0 or |B|=0|A|=0 \text { or }|B|=0

Therefore we can write,

|A||B|=0|A||B|=0

This implies,

A·B=0A \cdot B=0

This gives the always true condition that is when $A$ is perpendicular to $B$.