Question

Consider the plane R2 and consider any two lines that pass through the origin. Are these lines subspaces of the plane? Are they isomorphic? Are they "the same"? Clearly the "look different", but mathematically, do they behave the same structurally? Now consider the space R3 and now consider any two planes that pass through the origin of this space. Are these planes isomorphic? Are you placing too much emphasis on the "names" of the elements as opposed to the substructure?

Answer 1

http://www.cramster.com/answers-nov-11/algebra/math-linear-algebra-plane-r2-lines-pass_1739771.aspx?rec=0