I know that vectors are objects that have both magnitude and direction. Let's say we have a vector r that represents a house as an example, and it is r = [a, b, c] (a=number of rooms, b=number of floors, c=price). For this vector the idea of finding its magnitude does not make any sense to me, what would it mean? Also what would the direction or the angle between two house vectors mean?
What do vector size and direction really mean in vectors that are not position vectors
linear algebravectors
Best Answer
Not all vector spaces have a sensible dot product, and thus not all vector spaces have a sensible notion of length and direction (other than two vectors being or not being parallel, and one vector being longer or shorter than another, parallel vector).
Your vector space is a case of this, where the non-existence of a sensible dot product is a result of the application, rather than a mathematical inability to impose any dot product on the space. (A vector space where we mathematically cannot impose a dot product implies the negation of the axiom of choice. So that's not an easy thing.)