I have to determine the orthogonal projection of the vector v=(2, 4, 2) on the subspace Span(v1, v2). I know that V=(v1, v2, v3) where v1=(1, 0, 1), v2=(5, 1, 1,) and v3=(4, -1, 0). So far I have applied the Gram-Schmidt process on V to determine an orthonormal basis where, u1=(1/√2, 0, 1/√2), u2=(2/3, 1/3, -2/3) and u3=(√2/6, -2√2/3, -√2/6). I have tried using the projection formula once more:
proj_span(v)=((v.u1)/(u1.u1)).u1+(v.u2)/(u1.u2)).u2
and get an ortogonal vector of (26/9, 4/9, -2/3). So my question is, is this true or am I completely off track? Thanks in advance.