I often hear them used interchangeably ... they are very complicated to make any use of.
One way to think of the Euclidean plane is as a set of points satisfying certain relationships, expressible in terms of distance and angle.
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?