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Thread Subject:
Urgent- Equation of a plane in point normal form - Please help

Subject: Urgent- Equation of a plane in point normal form - Please help

From: GAURAV

Date: 7 Jan, 2011 03:22:06

Message: 1 of 4

Hi!

I have two points 3D co-ordinates [794, 782, -885] and [794, 814, 868]. What will be the equation of the plane passing through these two points in 3D space i.e. effectively a line through this point and extended parallely to form a plane? Here, the x co-ordinate is constant. i.e. a plane parallel to the y-z view.

What will be the point and the normal co-ordinates for the points?

Would it be any one point for the point and normal [794,0,0]?? It doesnot quite work out though.

Please help me out.

Thanks,
Regards,
Gaurav

Subject: Urgent- Equation of a plane in point normal form - Please help

From: John D'Errico

Date: 7 Jan, 2011 04:03:07

Message: 2 of 4

"GAURAV " <gsharda@engineering.uiowa.edu> wrote in message <ig60su$2i9$1@fred.mathworks.com>...
> Hi!
>
> I have two points 3D co-ordinates [794, 782, -885] and [794, 814, 868]. What will be the equation of the plane passing through these two points in 3D space i.e. effectively a line through this point and extended parallely to form a plane? Here, the x co-ordinate is constant. i.e. a plane parallel to the y-z view.
>
> What will be the point and the normal co-ordinates for the points?
>
> Would it be any one point for the point and normal [794,0,0]?? It doesnot quite work out though.

There are infinitely many planes through these two points.

If you wish to find the plane that is parallel to the yz plane,
where x = 794, then an arbitrary point in that plane is

  [794 0 0 ]

and the normal vector to that plane will indeed be

  [1 0 0]

So what does not work out?

John

Subject: Urgent- Equation of a plane in point normal form - Please help

From: GAURAV

Date: 7 Jan, 2011 04:45:21

Message: 3 of 4

Hi John!

Hey! Yes it does work.
Actually, it was my mistake. I need a plane parallel to the line joining the two points. So the normal to that plane wont be [1,0,0], right? Because the y and z co-ordinates are different. Had one of them be the same then that would have worked out, I guess.
But, I want a plane parallel to the line joining the two points.
How to go about it?
Appreciate your response.

Thanks,
Gaurav
"John D'Errico" <woodchips@rochester.rr.com> wrote in message <ig639q$76v$1@fred.mathworks.com>...
> "GAURAV " <gsharda@engineering.uiowa.edu> wrote in message <ig60su$2i9$1@fred.mathworks.com>...
> > Hi!
> >
> > I have two points 3D co-ordinates [794, 782, -885] and [794, 814, 868]. What will be the equation of the plane passing through these two points in 3D space i.e. effectively a line through this point and extended parallely to form a plane? Here, the x co-ordinate is constant. i.e. a plane parallel to the y-z view.
> >
> > What will be the point and the normal co-ordinates for the points?
> >
> > Would it be any one point for the point and normal [794,0,0]?? It doesnot quite work out though.
>
> There are infinitely many planes through these two points.
>
> If you wish to find the plane that is parallel to the yz plane,
> where x = 794, then an arbitrary point in that plane is
>
> [794 0 0 ]
>
> and the normal vector to that plane will indeed be
>
> [1 0 0]
>
> So what does not work out?
>
> John

Subject: Urgent- Equation of a plane in point normal form - Please help

From: Steven_Lord

Date: 7 Jan, 2011 14:53:59

Message: 4 of 4



"GAURAV " <gsharda@engineering.uiowa.edu> wrote in message
news:ig65p1$gcd$1@fred.mathworks.com...
> Hi John!
>
> Hey! Yes it does work. Actually, it was my mistake. I need a plane
> parallel to the line joining the two points.
>
> So the normal to that plane wont be [1,0,0], right? Because the y and z
> co-ordinates are different. Had one of them be the same then that would
> have worked out, I guess.
> But, I want a plane parallel to the line joining the two points.

You still have an infinite number of planes to choose from.

Place a pencil on a table. Consider that your line. Now what plane
parallel to that line do you want? Is it the surface of the table on which
the pencil rests? Is it the floor of the room in which the table is located
(assuming the table is level?) Is it the floor of the next room above or
below the room in which the table is located? Now orient the pencil so that
it's pointing along one of the walls. Is the wall that points in the same
direction as the pencil the parallel plane you're looking for? If the room
is rectangular, is it the corresponding wall on the other side of the room?

I hope that this shows you that your problem is not yet well-posed. You
need more information to choose which of those planes is the right one for
your problem.

--
Steve Lord
slord@mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlab.wikia.com/wiki/FAQ
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

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