Can R^2 Represent Planes Other Than the xy Plane in R^3?

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SUMMARY

In the context of R^3, R^2 specifically refers to the xy plane, defined as W={(a1, a2, 0): a1, a2 from R}. The discussion clarifies that while R^2 is inherently a two-dimensional plane, it is not accurate to claim that it can represent planes other than the xy plane without a defined context. The statement from the book is upheld as true, emphasizing the necessity of defining the plane's position in three-dimensional space.

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loli12
Can R^2 be planes other than the xy plane if it is not defined?
Because I got this statement which the book claims it to be false.

Let W be the xy plane in R^3; that is, W={(a1, a2, 0):a1, a2 from R). R= field of real numbers. Then W=R^2.

is there any other reason to make this statement false?
 
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R2 is just a two dimensional plane, you can put it anywhere you want.
 

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