If `abs(vec(a)+vec(b))=abs(vec(a)-vec(b))`, then show that `vec(a) and vec(b)` are perpendicular to each other.

Explanation

`vec(a).vec(b)= ab cos theta `
`vec(a) . vec(a) = a a cos theta = a^(2)`
`a^(2) = vec(a). vec(a)`
Similarly , `(A+B)^(2) = (vec(A)+vec(B)) . (vec(A)+vec(B)) = A^(2) +B^(2) + 2AB cos theta `
`(A - B)^(2) = (vec(A) - vec(B)) . (vec(A) - vec(B)) = A^(2) +B^(2) - 2AB cos theta `
where `theta ` is the angle between `vec(A) and vec(B)`
Given that the magnitude of `(vec(A)+vec(B))` = Magnitude of `( vec(A) - vec(B))`
`A^(2) + B^(2) + 2AB cos theta = A^(2) + B^(2) - 2AB cos theta `
`4AB cos theta = 0 , cos theta = 0 , theta = 90^(@)`