Let V be R

3

with the inner product

<v, w> = 3v1w1 + 2v2w2 + v3w3

where v = (v1, v2, v3) and w = (w1, w2, w3).

Find the orthogonal complement of the subspace U where

U = {(v1, v2, v3) element of V such that 2v1 - v2 = v3}.

Hi i understand that an orthogonal complement space it looks like this:

U complement = (v element of V : <u, v> = 0 for all u element U)

and that:

<v+w,u>=<v,u>+<w,u>=0+0=0

they just havent given me any usefull examples and only 2 examples. so help is needed please thnx