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From: Junghyun on 14 May 2010 00:20
Hi, Roger

Can I ask another question?
How can I define a plane equation just given 2 eigen-vectors (in 3D space) and a center point (also in a 3D space)?

Thank you.
Junghyun



"Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <hnoekl$a3e$1(a)fred.mathworks.com>...
> "Junghyun " <wkhdntnkpst(a)yahoo.com> wrote in message <hnni13$rja$1(a)fred.mathworks.com>...
> > Hi, Roger,
> > Thank you so much!
> > Your speculation was absolutely correct.
> >
> > a and b are unit vectors and not parallel but orthogonal.
> > Can I use either way for the case?
> > ........
> ------------
> Yes, either way will work for your unit orthogonal vectors.
>
> Roger Stafford
From: Roger Stafford on 14 May 2010 00:49
"Junghyun " <wkhdntnkpst(a)yahoo.com> wrote in message <hsij24$dk9$1(a)fred.mathworks.com>...
> Hi, Roger
>
> Can I ask another question?
> How can I define a plane equation just given 2 eigen-vectors (in 3D space) and a center point (also in a 3D space)?
>
> Thank you.
> Junghyun

If the two eigenvectors are u and v, then w = cross(u,v) is a vector orthogonal to each of these. A plane containing u and v is orthogonal to w. Therefore the equation of such a plane that also contains a given (center) point c is:

wx*x + wy*y + wz*z = w1*cx + w2*cy + w3*cz

where (wx,wy,wz) are the elements of w and (cx,cy,cz) are the coordinates of the point.

Roger Stafford
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