Solving 3D Vector equations
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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.
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Andrew Newell
2011-5-30
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.
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);
更多回答（1 个）
Jan
2011-5-28
2 个投票
Yes. If the equation can be solved, it can be solved in Matlab also.
If you want a more detailed answer, post the equation.
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