If You have the vector (a, b, c) then it is orthogonal to all of the vectors on the plane in R^3 defined by ax + by +cz= 0, because (a, b, c) •(x, y, z) = 0. Also if you have the plane in r^3 given by ax +by +cz =0, then the vector (a, b, c) is orthogonal to all the vectors on this plane. Did you show this method to find the orthogonal compliment because it is generalizable to higher dimensions?
You said that W perp is perpendicular to the original 1/2*x line, but there are infinite lines that are perpendicular. Is W perp the one you chose because it goes through the origin because vector spaces and subspaces must contain the 0 vector?
And how does y = y and z = z. There is no logical transition. It might seem obvious, but there are skipped steps. Pretend you are creating a video that explains this to a child.