Yes. The result is the total displacement that would result in following each vector in turn.
The above diagram shows the result of adding
The bottom diagram shows the result of adding
a + (b + c) = (a + b) + c
The rule works in all dimensions. Mostly the geometric vectors of computer graphics are two dimensional and three dimensional (although, in general, higher dimensions are possible).
The associative property means that sums
of several vectors can be
written like
Say that you walk five blocks north, and then three blocks east.
If, instead, you had walked three blocks east and then five blocks north would you arrive at the same place?