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?

There's not a unique definition for Euclidean space, but usually it's the set of all n-tuples of real numbers $R^n = { {(x_1, ..., x_n) : x_i \in R} } $ with some 'structure' define on it that allows one to measure angles and lenghts, like a inner product space or a metric. The set $R^n $ with it's usual operations of sum and scalar multiplication is a example of vector space over $R $, and it can be shown that every finite-dimensional vector space over $R $ is isomorphic to some Euclidean Space, meaning that in pratice every vector space (of finite dimension) is 'equal' to a Euclidean Space
