How to Mathematically describe a plane?

[HMPARTICLE]

The linear combinations of V = (1,1,0) and W = (0,1,1) fill a plane.
My question is how do i describe that plane? (not geometrically).

 

[WWGD]

This plane is the set { s(1,1,0)+t(0,1,1): s,t Reals}={(s, s+t, t)} . Is that what you are looking for?

 

[HMPARTICLE]

Yes! I understand what the question is asking now! I'm making that transition between A-level and UG.

Thanks WWGD.

 

[HallsofIvy]

Notice that the cross product is <1, 1, 0> and <0, 1, 1> is <1, -1, 1> and, since this plane contains the origin, it could also be described by the single equation x- y+ z= 0.