Proving the associative property of vector addition

[Specter]

Homework Statement

Give an example of the associative property of vector addition using vectors in Cartesion form.

Homework Equations

(u+v)+w=u+(v+w)

The Attempt at a Solution

I can't figure out how to get the arrow on top of my work so I wrote it without it.

I'm somewhat confused on why I am not getting the same answer for both like I should be. Did I make some stupid mistake in my work that I can't see, or does it have something to do with the coordinates that I chose to use?

u=(2,1), v=(3,2), w=(-2,1)

(u+v)+w=(2+3,1+3)+(-2,1)
=(5,4)+(-2,1)
=(5-2,4+1)
=(3,5)

u+(v+w)=(2,1)+(3-2,2+1)
=(2,1)+(1,3)
=(2+1,1+3)
=(3,4)

 

[PeroK]

u=(2,1), v=(3,2), w=(-2,1)

(u+v)+w=(2+3,1+3)+(-2,1)

That was not too hard to spot!

 

[Specter]

That was not too hard to spot!

Damn... I checked so many times too. Thank you!

 

[RPinPA]

I can't figure out how to get the arrow on top of my work so I wrote it without it.

Use \vec. It's explained in the LaTeX primer page, https://www.physicsforums.com/help/latexhelp/

$\vec u$ will produce $\vec u$.