Let $ u$ and $ v$ be vectors in $ \mathbb R^n$ . The exercise is to prove that if $ ||u+tv|| \ge ||u||$ for all real $ t$ , then $ u\cdot v=0$ ($ u$ and $ v$ are perpendicular).

I tried writing $ v$ as $ (n+xu)$ , where $ u\cdot n=0$ , and then try to prove that $ x$ must be zero, but was unable to develop this solution.