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Re: A simple Solve gives me errors

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From	Alexei Boulbitch <Alexei.Boulbitch@iee.lu>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Re: A simple Solve gives me errors
Date	Thu, 24 Apr 2014 08:03:37 +0000 (UTC)
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I want to find the center C of a circle in 3D where the plane is defined
by points p1,p2,p3. I wrote this:

p1 = {p1x, p1y, p1z}; (* tell it that p1,p2,p3 are vectors          *)
p2 = {p2x, p2y, p2z}; (* center of circle ctr = f p1+g p2+(1-f-g)p3 *)
p3 = {p3x, p3y, p3z}; (* keep the center in the plane of p1,p2,p3   *)

ctr = f p1 + g p2 + (1 - f - g) p3;
eq1 = (ctr - p1).(ctr - p1) - (ctr - p2).(ctr - p2) := 0;
eq2 = (ctr - p1).(ctr - p1) - (ctr - p3).(ctr - p3) := 0;

I get errors of a type I've seen before:

SetDelayed::write: Tag Norm in Norm[{-p1x+f p1x+g p2x+(1-f-g) p3x,-p1y+f
p1y+g p2y+(1-f-g) p3y,-p1z+f p1z+g p2z+(1-f-g) p3z}] is Protected. >>

And a similar one. I don't know what to do about this.
I want to do
Solve[{eq1, eq2}, {f, g}]

Hi,

It is just == instead of := and everything works. Try this:

p1 = {p1x, p1y, p1z};   (*tell it that p1,p2,p3 are vectors*)
p2 = {p2x, p2y, p2z};   (*center of circle ctr=f p1+g p2+(1-f-g)p3*)
p3 = {p3x, p3y, p3z};   (*keep the center in the plane of p1,p2,p3*)
ctr =f p1 + g p2 + (1 - f - g) p3;
eq1 = (ctr - p1).(ctr - p1) - (ctr - p2).(ctr - p2) == 0;
eq2 = (ctr - p1).(ctr - p1) - (ctr - p3).(ctr - p3) == 0;

Solve[{eq1, eq2}, {f, g}]

But the returned result is very long.

Nave fun, Alexei



Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
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Office phone :  +352-2454-2566
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e-mail: alexei.boulbitch@iee.lu

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Re: A simple Solve gives me errors Alexei Boulbitch <Alexei.Boulbitch@iee.lu> - 2014-04-24 08:03 +0000

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