Ted123 said:(i.e. points that are multiples of [itex](1,1,1)[/itex])
No, the equation [itex]x+y+z=0[/itex] is not the xyz-plane. It is a two-dimensional equation in three variables and represents a plane in three-dimensional space.
The xyz-plane, also known as the Cartesian plane, is a two-dimensional coordinate system in which a point is located by its distance from three perpendicular axes: the x-axis, y-axis, and z-axis.
No, the xyz-plane cannot be represented by a single equation. It is a two-dimensional space and therefore requires two variables to define a point on the plane.
The xyz-plane is a fundamental concept in mathematics and is used to graph and analyze equations in three-dimensional space. It also serves as the basis for many geometric and algebraic principles.
Yes, the concept of the xyz-plane can be extended to higher dimensions, such as four-dimensional space. In this case, additional axes (w-axis, for example) would be added to the coordinate system to represent the extra dimension.