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I know that we use three non-linear (at least one of them not linear) dots to define a 3d plane, but how do we define a 2 dimensional plane ? I am very bad at math and yes I have searched that in the google but can't find anything, maybe that is a dumb question and we don't define planes in 2D, I don't really know.

Thanks for answers, I really need them.

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  • $\begingroup$ I think a plane is determined by two intersecting lines $\endgroup$
    – gd1035
    Commented Nov 15, 2018 at 20:09
  • $\begingroup$ If we write like that plane is defined like that : en.wikipedia.org/wiki/Plane_(geometry), but I am trying to learn how do we define it in the math language, thanks anyway. $\endgroup$ Commented Nov 15, 2018 at 20:11
  • $\begingroup$ In that case, a plane will be determined by the span of two linearly independent vectors. $\endgroup$
    – gd1035
    Commented Nov 15, 2018 at 20:13
  • $\begingroup$ If by "3d plane", you are referring to a plane in $\mathbb{R}^3$, then "2d plane" isn't very meaningful because a "plane" in $\mathbb{R}^2$ is simply all of $\mathbb{R}^2$. $\endgroup$
    – tsooch
    Commented Nov 15, 2018 at 20:14
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    $\begingroup$ @UmutPiynar I mean $\mathbb{R}^2$ itself is the plane. $\endgroup$
    – tsooch
    Commented Nov 15, 2018 at 20:18

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We often talk about “a plane in 3D”. This is probably what you meant when you said “a 3D plane”. A plane is a 2D object, so when we are thinking in 3D we need to define which plane we mean by referring to some points (or lines as mentioned in the comments). In 2D the whole thing is a plane unless it’s curved like the surface of the earth or something. So there’s really nothing to define.

The crucial word is “in” - think of the plane occupying part of the 3D space. So it’s not a 3D plane, but a plane in (or embedded in) 3D.

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  • $\begingroup$ excellent way of describing. $\endgroup$
    – Sedumjoy
    Commented Sep 8, 2022 at 18:03

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