Why can a vector not be used to define a plane, why does it have to be a vector and a point. Couldn't you just take a vector and draw a plane at the tip which is perpendicular to the "stem" of the vector in all directions?
2026-04-12 20:50:01.1776027001
Why Can a Plane Not Be Defined Solely With a Vector
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A plane through the origin can always be described this way, but a description like this cannot distinguish between a plane through the origin and a parallel translate of the same plane.
I like to emphasize that in the setting of multivariable calculus, a vector that is thought of as an arrow doesn't really have a base point; it doesn't 'start somewhere'. It's really only a direction and a magnitude