## Inner product space

### Inner product space

Hi everyone!

I faced with a problem: prove that two vectors of inner product space is on the same ray only when $\left \| x+y \right \| = \left \| x \right \| + \left \| y \right \|$.

Does anyone know how to prove it?

I faced with a problem: prove that two vectors of inner product space is on the same ray only when $\left \| x+y \right \| = \left \| x \right \| + \left \| y \right \|$.

Does anyone know how to prove it?

- Tolaso J Kos
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**Posts:**866**Joined:**Sat Nov 07, 2015 6:12 pm**Location:**Larisa-
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### Re: Inner product space

**Hint:**Equality holds when vectors are parallel i.e, $u=kv$, $k \in \mathbb{R}^+$ because $u \cdot v= \|u \| \cdot \|v\| \cos \theta$ when $\cos \theta=1$, the equality of the Cauchy-Schwarz inequality holds.

**Imagination is much more important than knowledge.**

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