Difference between Euclidean space and vector space? I often hear them used interchangeably ... they are very complicated to make any use of.
Wikipedia words:
Euclidean space:

One way to think of the Euclidean plane is as a set of points satisfying certain relationships, expressible in terms of distance and angle.

Vector space:

A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context.

They are not related at all. A vector space is a structure composed of vectors and has no magnitude or dimension, whereas Euclidean space can be of any dimension and is based on coordinates.
I hear 3-D programming uses vectors, so Euclidean geometry should be useless, no?
Basically, aren't they unrelated?

While a vector space is something very formal and axiomatic, Euclidean space has not a unified meaning. Usually, it refers to something where you have points, lines, can measure angles and distances and the Euclidean axioms are satisfied. Sometimes it is identified with $\mathbb{R}^2$ resp. $\mathbb{R}^n$ but more as an affine and metric space (you have both points and vectors, not just vectors). So, the Euclidean space has softer meaning and usually refers to a richer structure.
