Final answer:
Without additional information regarding set w and how the product is defined for its vectors, specific vectors u and v cannot be provided to demonstrate that their product does not belong to set w, as required to show that w is not a vector space.
Step-by-step explanation:
The question refers to whether a set of vectors forms a vector space. It is a principle in linear algebra that in a vector space, the addition of any two vectors or the scalar multiplication of any vector must result in another vector that is also in that space. To prove that a set does not form a vector space, you can show that there exists at least one pair of vectors whose product (or addition, depending on the operation defined in the space) does not result in a vector in the same set.
In this particular case, we want to find two specific vectors, u and v, belonging to set w, such that the product of u and v (denoted as uv) does not result in a vector that is within set w. Unfortunately, without more information on how the product of two vectors is defined in this set or what set w precisely consists of, we cannot provide specific vectors u and v. Normally, a 'product' of vectors is not standard outside of certain contexts like the dot or cross product, which both have very specific definitions and properties in vector spaces.