Cosets in ℝ3 Using the following definition, in Problem, find the -cosets for the given ve...

Cosets in ℝ3 Using the following definition, in Problem, find the -cosets for the given vectors and give a graphical description of each.

Cosets

If is a subspace of vector space ℝn that includes the origin, and is a vector in ℝn, then the -coset of , denoted , is the set defined by

Thus, in ℝ3, if is a plane passing through the origin, then the coset is a plane parallel to passing through .