Re: A simple Solve gives me errors

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• Subject: [mg132631] Re: A simple Solve gives me errors
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Thu, 24 Apr 2014 04:03:35 -0400 (EDT)
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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. >>

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,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

```

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