Question

| vector a + vector b | = | vector a - vector b| then angle between vector a and vector b

Answer 1

let us assume that |A+B|=|A-B| are non-zero vectors..
squaring both sides
|A+B|²=|A-B|²
|A|²+2AB+|B|²=|A|²-2AB+|B|²
|A|² and |B|² will cancel out each other
4AB=0
A.B=0
|A||B|cos theta =0
as cos 90°=0
we can say that A and B are perpendicular or angle bwtween them is 90°.
hope it helps..