Mathematically, the number of possible unique vectors in a d-dimensional space is given by:

d^n

where d is the number of dimensions and n is the number of vectors.

For example, in a 3-dimensional space, there are 3^3 = 27 possible unique vectors. In a 10-dimensional space, there are 10^10 possible unique vectors. And in a 100-dimensional space, there are 100^100 possible unique vectors.