Finding an unknown vector from three known vectors

Hi, I have some problem in writing the code. Let say I have vector A = [125 350 -80], B=[-115 350 -80], D=[-15 530 545] and I need to determine the positon of vector C. The lengths/magnitudes are given which are CA=300, CB=300, CD=650. How do I determine the value for C1 C2 C3?

[Bruno Luong]

Keyword: Trilateration

Answer 1

[David Hill]

syms x y z;
C=[x,y,z];
A = [125 350 -80]; 
B = [-115 350 -80]; 
D = [-15 530 545];
eq1=norm(A-C)==300;
eq2=norm(B-C)==300;
eq3=norm(D-C)==650;
eqns=[eq1,eq2,eq3];
c=vpasolve(eqns,[x,y,z]);

[Aliff Firdaus Suhaimi]

Thanks for your help! I'm doing it wrong before this. Since vpasolve only give one solution I add initial values so that it will give me the answer that I want.

Right now I'm trying to make for loop as the value of CD is decreasing with increment -5 until 550. What I did below give me the same result for every looping. I can't seem to figure out where is the wrong part.

clear
close all
clc
syms x y z;
C=[x,y,z];
A = [125 350 -80]; 
B = [-115 350 -80]; 
D = [-15 530 545];
eq1=norm(A-C)==300;
eq2=norm(B-C)==300;
eq3=norm(D-C)==650;
eqns=[eq1,eq2,eq3];

for n=1:1
C=vpasolve(eqns,[x,y,z],[5;500;-90]);
end

for eq3=650:-10:550
ansx=['Cx',C.x];
disp (ansx)
ansy=['Cy',C.y];
disp (ansy)
ansz=['Cz',C.z];
disp (ansz)
end