Geometry: Planes, x+y+z=0 - How Does It Work?

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The equation x+y+z=0 represents a plane in three-dimensional space, despite being a two-dimensional object. A plane can be visualized in three dimensions, where it requires only two coordinates to define a point on it. This means that while a plane is fundamentally two-dimensional, it can be expressed within higher-dimensional spaces using additional variables. Understanding this concept clarifies the relationship between dimensions and how planes can be represented in various contexts. The discussion emphasizes the nature of planes and their dimensional properties.
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I do not understnad how x+y+z=0 can be a plane, I thought a plane has 2 dimensions, this is all :) thanks.
 
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A plane is a two dimensional object, but it can be rotated into three dimensions. Another way of looking at it is that you only need two coordinates to express a point on the plane (hence it being 2-dimensional), but it can be embedded in a space consisting of an arbitrary amount of dimensions, in which case you could need more variables to express it.
 
Vorde said:
A plane is a two dimensional object, but it can be rotated into three dimensions. Another way of looking at it is that you only need two coordinates to express a point on the plane (hence it being 2-dimensional), but it can be embedded in a space consisting of an arbitrary amount of dimensions, in which case you could need more variables to express it.

Ahh of course - cheers !
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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