Under what condition the sum and difference of two vectors will be equal in magnitude ?

Explanation

`|vec(A) + vec(B)| = |vec(A) - vec(B)|`
Squaring both sides
`A^(2) + B^(2) + 2vec(A) * vec(B) = A^(2) - 2vec(A) * vec(B) + B^(2)`
`4 vec(A) * vec(B) = 0 (or)`
`vec(A) * vec(B) = 0 i.e., vec(A) bot vec(B)`
Thus , when the two vectors are equal in magnitude and perpendicular to each other. then the sum and difference of two vectors will be equal in magnitude .