Problem : Prove that each plane that intersects the origin of the vector space $R^3$ is a subspace of $R^3$
I've tried to tackle this by showing that the subspace is not empty, that is closed under vector addition and scalar multiplication, but I'm not sure how to define the subspace mathematically.
Best Answer
a plane in $R^3$ has a unique(except for a sign) unit normal, say, $(a,b,c).$ the equation of the plane is $\{(x,y,z): ax+by+cz = 0\}$ show that if two points in the plane then their sum and scalar multiples are also on the plane.