Populations of each of the fifty US states is a vector?

[cdot]

My calculus textbook says the populations of each of the fifty states is a vector quantity. I know what a vector is but I'm not grasping this particular example. Any help? I would think that maybe it's because the populations may increase or decrease but I thought a vector quantity was associated with a direction in three dimensional space.

 

[Mark44]

My calculus textbook says the populations of each of the fifty states is a vector quantity. I know what a vector is but I'm not grasping this particular example. Any help? I would think that maybe it's because the populations may increase or decrease but I thought a vector quantity was associated with a direction in three dimensional space.

They are probably talking about a vector whose components are the populations of the states.

Vectors are not limited to 3D space. They can exist (at least mathematically) in spaces of dimension 1, 2, 3, 4, and as high as required. We normally think of one-, two-, and three-dimensional spaces (a line, a plane, space, respectively), but just because we can't envision 11-dimensional space, for example, that doesn't mean that there isn't an application for it. There are even infinite-dimension vectors whose components consist of the terms in an infinite sequence of numbers.