BASE O(i,jk) and u(a,b,c)

let u(i',j',k) or i',j',k' are unit vectors of the basis u. O(i,j,k) or i,j,k are the unit vectors of the basis O. I want to link the basis u to the vector i of the basis O where i is the origin of the basis u.But i and c are collinear even if i is rotated. Make a Represent with matlab code

[Torsten]

At least for me it's impossible to understand what your question is.