   Conservation of torque
  I have a super simple (I guess) problem that I somehow cannot solve:BasicallyAxF = BxGWhere x is the crossproduct operator and A,B are position vectors and F,G are forces. I know A,B and G and I need to know the analytical componentwise solution to F ie what Fx,Fy,Fz are in terms of Ax,Ay,Az,Bx,By,Bz,Gx,Gy,Gz.My intuition tells me the componetwise solution must be symmetrical for x,y,z but my solution is not so it must be wrong, right?// Bucko 
  A x B = C=> B = C x Aso, F = (B x G) x Adoes that sounds right? ;  There is no single solution to the equation. The only thing you can  say is that F must be in the same plane as A, B and G, but the direction and magnitude can not be uniquely determined.;  Sounds like it needs another constraint on the solution. Maybe requiring that F is at a right angle to A, or F has the same magnitude as G? ;  Yes, if F is taken to be orthogonal to A the solution isF = (B x G) x A / |A|²Of course, this only works if A lies in the same plane as B and G.;  Forgive me for being stupid but this is three linear equations with three unknowns and should as far as I know be solvable:A x F = B x G (A,B are vectors, F,G are force vectors, all known but F)(1) AyFz - AzFy = ByGz - BzGy(2) AzFx - AxFz = BzGx - BxGz(1) AxFy - AyFx = BxGy - ByGxFx, Fy, Fz are the unkowns, all else are known.Given a certain torque (B x G), what force (F) should I apply at A to keep the system in zero torque?I need this for my Hitman style verlet ragdoll to keep constraints working with 3 points from generating torque.// Bucko  ;  You have three linear equations and three unknowns, yes, but as you see when you try to solve it, the system is not well determined.(Or viewed as a matrix equation: Ax=y, the matrix A is square but not invertible in this problem.);  I see, I need another constraint then.I thought of using impulse conservation as a constraint but as far as I can tell it will not help me either as it would add three equations and three unkowns for the force applied at origo.A x F = B x GandF + G + H = 0Where H is the force applied at the point from where I measure A and B. Shit, need to come up with something a bit more clever then eh?// Bucko 