how would you define a 3-D plane?

Question

im at school and one of my friends is wondering

Answer 1

As a plane is two-dimensional by definition (there are no 3-D planes), I assme you are looking for a description of a plane in 3-space.

In mathematical terms, the general equation of a plane is:

Ax + By + Cz + D = 0

A useful variation is the intercept form of the equation which is:

x/a + y/b + z/c = 1

where a = -D/A, b = -D/B, c = -D/C.
Here, a is the x-axis intercept, b the y-axis intercept and c the z-axis intercept of the plane.
Of course, any of A, B or C could be zero: this will still be a plane. For example, x+y=1 defines a plane. Since there is no z component, we know that this plane is parallel to the z axis (ie, there is no z-axis intercept.) x=1 also defines a plane which is parallel to both the y and z axes. Therefore not all three variables need to occur in the function of a plane.

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SEE : http://mudandmuck.com/str2/plane.htm
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The equations for the planes shown here are in a third form,
z=f(x,y).

They are:
z = 1
z = 1 - y
z = 1 - y - x

Answer 2

A 3-d plane, 3 demensional real life plane or model, though if you where talking about a video game or picture in my mind i think of it as a 2-d plane, becuase i have to be able to see all around it, There fore if its a model or plane you must be able to see all around it to be a 3-d plane.

Not very mathamatical but easy to understand

Answer 3

A plane is two-dimensional by definition. It stretches infinitely in two dimensions. A three dimensional plane would be the whole universe!

Answer 4

As a real plane

Answer 5

Nick Garrity

Answer 6

For a simple orthogonal coordinate system (e.g. x,y,z), the equation of the plane must be a function of all three variables.