Show that the set of all points in the plan ax + by + cz = 0 is a subspace of R^3. Find vector v1 and v2 such that [v1, v2] is the plan 2x - 3y + 4z = 0
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