Let $(\cdot,\cdot)$ be a scalar product on a finite dimensional vector space and let $0\ne v,w$ be two vectors of the same length, i.e. $(v,v)=(w,w)$.
Visually, it seams to me clear that the angle formed between $v$ and $w-v$ must be obtuse, i.e. that $(v,w-v)\le 0$.
How to prove this formally? (Or is this statement false?)