See if this resolution is correct?
belongs to the subspace of R^3
belongs to the subspace of R^3
Is correct?
The solution looks correct but you need to clarify some things, firstly your two vectors should be any two vectors I think you may have implied this but i am confused by your notation here. Also you haven't given a reason using the vector space properties or the equation of the plane for why the sum belongs to the plane. You have also forgot to make any mention of the zero vector.
Bobak