Given u and v be non-collinear vectors in R2 and w be the orthogonal projection vector of u on v. Any vector in R2 can be written as linear combination of u and v because u≠λv for any constant λ. Hence, {u,v} set is linearly independent but w can not be written as au+bv because w.u≠0 and w.v≠0, which is contradiction of orthogonal projection concept.