Help with a basic linear algebra proof

[paulrb]

Homework Statement

Let x and y be nonzero vectors in Rn. Prove ||x+y|| = ||x|| + ||y|| if and only if y = cx for some c > 0.

Homework Equations

Formula for vector magnitude, basic properties of vectors, possibly other vector formulas

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.

 

[Mark44]

Isn't ||x + y||^2 = (x + y) . (x + y)?

 

[paulrb]

Thank you, that was enough for me to figure it out :)