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binbagsss

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In summary, a plane may be a two-dimensional object, but it can also be rotated into three dimensions. This is because while it only requires two coordinates to express a point on the plane, it can be embedded in a space with an arbitrary amount of dimensions, potentially requiring more variables to express it.

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binbagsss

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Physics news on Phys.org

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Vorde

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binbagsss

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Vorde said:

Ahh of course - cheers !

A plane in geometry is a two-dimensional shape that extends infinitely in all directions. It is represented by a flat surface and has no thickness or depth.

A plane can be defined by an equation in the form of Ax + By + Cz = D, where A, B, and C are coefficients and x, y, and z are variables. This equation is known as the standard form of a plane.

This equation represents a plane passing through the origin, where the x, y, and z axes intersect. The coefficients of x, y, and z represent the direction and slope of the plane.

To graph a plane, you can use the intercept method by finding the x, y, and z intercepts and connecting them. Another method is using a set of three points that satisfy the equation and connecting them to form a triangle, which represents the plane.

The equation x+y+z=0 represents a specific plane in three-dimensional space. Any point (x, y, z) that satisfies this equation will lie on the plane. Conversely, any point on the plane can be substituted into the equation and it will be true.

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