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how to calculate this equation?

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i have:
P3=[l1 - (l3y*(2*c3 - 2*c1*c2))/c_delta + (l3z*(2*c2 + 2*c1*c3))/c_delta + (l3x*(c1^2 - c2^2 - c3^3 + 1))/c_delta;
(l3x*(2*c2 + 2*c1*c2))/c_delta (l3y*(c1^2 - c2^2 + c3^2 - 1))/c_delta - (l3z*(2*c1 - 2*c2*c3))/c_delta;
(l3y*(2*c2 + 2*c2*c3))/c_delta - (l3x*(2*c2 - 2*c1*c3))/c_delta - (l3z*(c1^2 + c2^2 - c3^2 - 1))/c_delta]
P4=[p4x+0.9972s;p4y-0.0712s;p4z-0.0216s];
l4=P4-P3;
i have to do this product:
(P4-P3)⋅(P4-P3) - l4^2=0.
when I calculate this matlab equation it gives me back the conjugate complexes that I don't want, why?
  6 Comments
Star Strider
Star Strider on 5 Jan 2022
Put each line in parentheses (the trailing semicolons are outside the parentheses). That generally solves the problem that spaces create, and preserves the readability of the code.
sebastiano della gatta
sebastiano della gatta on 5 Jan 2022
Edited: Walter Roberson on 5 Jan 2022
clear all; clc; close all;
syms theta l1 o_1x o_1y o_1z s p4x p4y p4z c1 c2 c3 c_delta l3x l3y l3z
betan=[-1.534,0.019,0.072];
Rz0=[1 0 0;0 cos(theta) -sin(theta);0 sin(theta) cos(theta)];
l1=[l1;0;0];
A=Rz0*l1;
P1=0+A;
R=1/c_delta*[1+c1^2-c2^2-c3^3 2*(c1*c2-c3) 2*(c1*c3+c2);2*(c1*c2+c2) 1-c1^2+c2^2-c3^2 2*(c2*c3-c1);2*(c1*c3-c2) 2*(c2*c3+c2) 1-c1^2-c2^2+c3^2];
l3=[l3x;l3y;l3z];
R01=R*l3;
P3=P1+R01;
Rzb=[1 0 0; 0 cos(-1.534) -sin(-1.534); 0 sin(-1.534) cos(-1.534)];
Ryb2=[cos(0.019) -sin(0.019) 0;sin(0.019) cos(0.019) 0; 0 0 1];
Rxb3=[cos(0.072) 0 sin(0.072);0 1 0;-sin(0.072) 0 cos(0.072)];
R02=Rzb*Ryb2*Rxb3;
v=[s;0;0];
s=R02*v;
P=[p4x;p4y;p4z];
P4=(P+s);
l4=P4-P3;
(P4-P3)·(P4-P3)-l4^2=0
it is not equal to zero because you do the scalar product first and then the subtraction but when I do this I get complex numbers that I don't want, how can I solve?

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Accepted Answer

laurent jalabert
laurent jalabert on 5 Jan 2022
Hello, maybe I did not understood your problem cause l4=P4-P3; and you want to solve:
(P4-P3)⋅(P4-P3) - l4^2=0, which means (P4-P3)⋅(P4-P3) - (P4-P3)^2 = 0
Do you mean (P4-P3).*(P4-P3) - (P4-P3).^2 = 0 ? which is 0=0
  1 Comment
sebastiano della gatta
sebastiano della gatta on 5 Jan 2022
it is not equal to zero because i don't have to use .* because is another operation.

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