prove that `(vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2)`, if and only if `vec(a),vec(b)` are perpendicular, given `vec(a) ne vec(0), vec(b) ne vec(0)`.

Answer

`vec(a)` and `vec(b)` are perpendicular