1. The problem statement, all variables and given/known data Let x and y be nonzero vectors in Rn. Prove ||x+y|| = ||x|| + ||y|| if and only if y = cx for some c > 0. 2. Relevant equations Formula for vector magnitude, basic properties of vectors, possibly other vector formulas 3. The attempt at a solution I have proved the first part, that is, that ||x+y|| = ||x|| + ||y|| if y=cx for some c > 0. Now I have to prove the second part: If ||x+y|| = ||x|| + ||y|| there is some c > 0 such that y = cx. I don't know how to begin proving this. I'm guessing I need to find c using the equation. However I can't think of a method that allows me to do this. If someone could give me hint or help me get started, I would greatly appreciate it. Thanks.