Discovering the Meaning of a Plane Equation in 4D | Homework Equations

[DespicableMe]

Homework Statement

If you add a fourth variable to a plane and wrote the entire plane equation as a scalar equation, what would that equation represent?

Homework Equations

I'm guessing the scalar equation would look something like Ax + By + Cz + Dk + E = 0

The Attempt at a Solution

I was thinking that it can't represent a shape. I can't visualize it.
Then another thought - what would a plane in 4D look like? What IS 4D?

I'm not sure what the above equation would represent in terms of planes.

 

[tiny-tim]

Hi DespicableMe!

I'm guessing the scalar equation would look something like Ax + By + Cz + Dk + E = 0
…
Then another thought - what would a plane in 4D look like? What IS 4D?

Yes, that's the right equation.

If the fourth dimension is time, that represents the equation of a moving plane, for example a plane wavefront.

 

[DespicableMe]

Hi DespicableMe!


Yes, that's the right equation.

If the fourth dimension is time, that represents the equation of a moving plane, for example a plane wavefront.

I also read somewhere that a fourth varible in a plane equation would express the relative distance of the (projection?) plane from a certain location.

What do you think of this?

 

[tiny-tim]

Ah, that's the constant in a 3D equation …

for example x + y + z + D = 0 is a plane whose distance from the origin is 2D/√3