Intersection between two hyperplanes

wintersolstice · 2010-12-31 02:02:06

I've struggling to figure out how to find out the intersection between two planes in 3D and above, if the equations have one equals sign (which means the plane are one less dimension than the space, and if they don't intersect they must be parallel) but with multiple equals signs I can't manipulate the equations to find the equation of the intersection. Does any know how to do it?

DrSteve · 2010-12-31 05:20:55

It might help if you post a specific example you're having trouble with.

bobbym · 2010-12-31 06:57:18

Hi wintersolstice;

I can give you a general solution for any two planes in ( x,y,z ). It utilizes vectors.

wintersolstice · 2011-01-01 07:39:50

bobbym wrote:

Hi wintersolstice;
I can give you a general solution for any two planes in ( x,y,z ). It utilizes vectors.

Well I know how to do that, because they only have one equals sign (and like I said I know how to do them using the cartesian equations)

Finding the intersection between lines in realmspace (or x,y,z:D space) is harder, because lines have two equals signs in their cartesian equation and the intersection doesn't always exist even when there not parallel. but a point (that's all the intersection is so, it's a co-ordinate not an equation) can always be found (when there's no intersection the point isn't on the lines) I saw how to find this point in a book but can't find it. (the book!)

The problem I'm facing (or one of them) is finding the intersection between two planes in tetraspace (or x,y,z,w) i.e. four axis. the equation of the plane has two equals signs and you face the same problem as you do with lines in realmspace.

the things is I don't know much about co-ordinate geometry in 3D and above, I can't even find the distance from a point to a line/plane or find the line perpendicular to a plane or vice-versa

I'm investiagtion stellation in the higher dimensions that's what this is for:D

bobbym · 2011-01-01 08:01:56

Hi wintersolstice;

wintersolstice wrote:

because lines have two equals signs in their cartesian equation

I am not following you here. Can you post what a typical problem is? I am not saying I can do it but perhaps someone else can.

wintersolstice wrote:

the things is I don't know much about co-ordinate geometry in 3D and above, I can't even find the distance from a point to a line/plane or find the line perpendicular to a plane or vice-versa

Maybe you could think about getting stronger in your understanding of coordinate geometry.
You could post some simpler problems that have the flavor of your bigger problem. Maybe it would give some insight.

wintersolstice · 2011-01-08 04:43:24

bobbym wrote:

Hi wintersolstice;
I am not following you here. Can you post what a typical problem is? I am not saying I can do it but perhaps someone else can.

I think these intersect (if I've worked them out right) there part of an investigation to stellate the hexadecachoron

I still don't know what the general equation for a plane is in tetraspace

bobbym wrote:

Maybe you could think about getting stronger in your understanding of coordinate geometry.
You could post some simpler problems that have the flavor of your bigger problem. Maybe it would give some insight.

I have considered that:D I didn't realise until I needed it how bad I was!

Math Is Fun Forum

#1 2010-12-31 02:02:06

Intersection between two hyperplanes

#2 2010-12-31 05:20:55

Re: Intersection between two hyperplanes

#3 2010-12-31 06:57:18

Re: Intersection between two hyperplanes

#4 2011-01-01 07:39:50

Re: Intersection between two hyperplanes

#5 2011-01-01 08:01:56

Re: Intersection between two hyperplanes

#6 2011-01-08 04:43:24

Re: Intersection between two hyperplanes

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