Please , I don´t know how to do this demonstration:

Question

If A and B are mutually perpendicular vectors( different to zero vector) and "c" is any number show that :
|| A +cB ||>= ||A||

Answer 1

let A be on x axis = a i + 0 j
then B put on y axis = 0 i + b j
(b could be - of course)

||A + cB|| = || sqrt(a^2 + c^2b^2 ||

which is >/= sqrt a^2