MATLAB: Solving 3D Vector equations

3dequationsMATLABsolvevector

I need to solve 3D vector equations having known and unknown position vectors. Equations have dot products, cross products, modulus and a combination of them.
Here's a one set of equations.
(l-o) x (q-o) . (c-o) = 0
o-q * [ (l-q).(q-c) ] = l-q * [ (o-q).(q-c) ]
Here, l,o,q,c are position vectors and l,o are known.
Thank you.

Best Answer

Interesting equations. The first says that the points l,o,q,c are coplanar, but I'm not sure what the second means.
You can solve a system like this using fsolve. Since fsolve requires a function f(x) with vector x, you first need to combine your unknowns in a vector, e.g., x = [q; c]. Note: I am assuming your vectors are all column vectors.
Create a function
function y = myfun(x,l,o)
q = x(1:3); c = x(4:6);
y = [dot(cross(l-o,q-o),c-o)
abs(o-q)*dot(l-q,q-c) - abs(l-q)*dot(o-q,q-c)];
To solve your system of equations, you need to find an x that makes y equal to zero. Save this function in a file.
In a separate file, provide the values for l and o and create an anonymous function:
f = @(x) myfun(x,l,o);
Then make an initial guess for your solution, e.g., q0 and c0. Finally, solve:
x0 = [q0; c0];
xsol = fsolve(f,x0);
Related Question