im dealing with a question in R3 where U is a subspace containing all vectors (x,y,z) satisfying x - y + 2z = 0.

Im having trouble picturing what U actually looks like geometrically, theses kind of things always seem to confuse me.

I need to describe the orthogonal complement U(perp) of U?

I also want to find the projections onto U and U(perp) of the vector (2, 1, 4)?

Needless to say im completely lost on where to start..

Any tips?