Question

Let S be the subspace of R3 spanned by the vectors ū1 = (2/3, 2/3, 1/3)^T and ū2 = (1/sqrt[2], -1/sqrt[2], 0)^T. Let x-vector = (1,2,2)^T. Find the projection p-vector of x-vector onto S. Show that (p-vector - x-vector) _|_ ū1 and (p-vector - x-vector) _|_ ū2.

_|_ = Orthogonal