Prove that `( veca+ vec b).( vec a+ vecb)= | veca|^2+| vec b|^2` , if and only if ` vec a ,vec b` are perpendicular, given ` vec a!= vec0, vec b!= vec0`

Explanation

`(vec(a) + vec(b)).(vec(a) + vec(b)) = |vec(a)|^(2)+|vec(b)|^(2)`
`implies |vec(a)|^(2) + |vec(b)|^(2) + 2vec(a).vec(b) = |vec(a)|^(2)+|vec(b)|^(2)`
`implies 2vec(a).vec(b) = 0implies vec(a).vec(b) = 0`
`implies vec(a)` and `vec(b)` are mutually perpendicular.
Hence Proved.