I'm beginning to learn some vector calculus, and I am slightly confused about the textbook's explanation of planes spanned by two vectors.
They said for example that the xy plane is an example of the plane spanned by i and j. This concept makes sense to me, but I'm just wondering if a plane needs to necessarily be defined by two vectors perpendicular to each other like the xy , yz , and xz planes.
Best Answer
No. For example, the vectors $(1,0)$ and $(1,1)$ also span the $xy$ plane. You only need two independent vectors to span the plane.