Do the given vectors form an orthogonal basis for R Yes the given set does form an orthogonal basis for R O No the given set does not form an orthogonal basis for R You are given the theorem below Let V V V be an orthogonal basis for a subspace W of R and let w be any vector in W Then the unique scalars c C such that W C V SKK are given by W V for i 1 k v V Use the theorem to express was a linear combination of the above basis vectors Give the coordinate vector w of w with respect to the basis B v V V of R w g V W 0 12 54 1 12