This is the original Spanish version of the exercise:
My understanding is that if we make a circle which has a center in [0,0] and a radius of 1 and we take all the points of that circle.... is this set of points a vector space?
How do they define addition of 2 members of a vector space? As a scalar product? If so, than the set is not a vector space since it is possible to do the scalar product of 2 such vectors, that the product will be out of the circle, so the set can't be a vector space...
I assume they meant the points of the circle are represented by vectors in the vector space, right?