Show that u and v are orthogonal if and only if (||u+v||)^2 = ||u||^2+||v||^2.

Question

Show that u and v are orthogonal if and only if (||u+v||)^2 = ||u||^2+||v||^2.

Answer 1

Here is a hint: rewrite || something ||^2 as the appropriate dot/inner product, expand and simplify.