Answer:
A vector space is a set of all points that can be generated by a linear combination of some integer number of vectors. A field is an abstract mathematical construct that is basically a set elements that form an abelian group under two binary operations, with the distributive property. Examples:
Euclidean space(x,y,z) is a vector space.
The rational and real numbers form a field with regular addition and multiplication.
Also, every set of congruence classes formed under a prime integer (mod algebra) is a field.