Is this any kind of proof?

[sponsoredwalk]

http://img405.imageshack.us/img405/8026/prover.jpg [Broken]

I would say it's pretty weak, how could I improve upon it?

It's supposed to be the triangle inequality.

 

[CompuChip]

I don't mean to be rude, but frankly: it's not a proof at all. It's just two columns with a list of things that seem to be unrelated, and something that looks like what you wanted to prove at the bottom.

How about you use the definition of norm, as
$$|\vec{v}|^2 = \vec v \cdot \vec v$$
and work out
$$|\vec{u} + \vec{v}|^2$$

 

[sponsoredwalk]

I'm just going off of the material presented in the chapter of a calc/linear algebra book, it is the first chapter and hasn't touched on anything further.

$$\overline{A} \overline{B} \ + \ \overline{B} \overline{C} \ = \ \overline{AC}$$

if I'm not mistaken, then I went to normalize the vectors but I think I got it wrong.

I'll just keep reading...