How many vectors do you need to form a basis?
Maybe forms a basis for the subspace?
So if there are 3 vectors needed to form a basis....
From Wikipedia article on dimension:
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.