Addition of vectors with triangle vertices

[ddtozone]

Homework Statement

If A, B, and C are the vertices of a triangle, find the following.
(A→B) + (B→C) + (C→A)

The answer has to be given like this:

_____ i + _____ j

2. Homework Equations (I think?)
a+b=b+a
a+(b+c)=(a+b)+c
a+0=a
a+(-a)=0
c(a+b)=ca+cb
(c+d)a=ca+da
(cd)a=c(da)
1a=a

The Attempt at a Solution

I'm not even sure what kind of solution this should look like. My best guess would be
<A+B+C>i + <A+B+C>j
Any better, more sensible ideas? Thanks!

 

[Dick]

The vector connecting A to B is given by the vector (B-A), where B and A are the coordinates of the points. Add up all three terms. What do you get?

 

[ddtozone]

Oh okay, so it all cancels out and comes to 0. That makes sense. Thank you!