The discussion revolves around a vector system involving sum and dot product equations. Participants are exploring the relationships between vectors and the implications of given equations in a potentially two-dimensional or three-dimensional context.
The discussion is active, with participants providing various interpretations and questioning the completeness of the information provided. Some guidance has been offered regarding the relationships between the vectors, but there is no explicit consensus on the approach or solution.
There are noted constraints regarding the lack of specification about the dimensionality of the problem and the nature of the vectors involved. Participants are also considering the implications of defining certain vectors as constants or variables.
You didn't specify whether this is a 2D or 3D problem. You also didn't specify that ##\vec u, ~ \vec v,~ m## are given constants and the unknowns are ##\vec x## and ##\vec y##. Is that correct? Certainly, if it is a 3D problem there can be many solutions. For example if ##\vec v = \langle 0,0,1\rangle## and ##m=0##, so ##\vec x## is perpendicular to ##\vec v## so ##\vec x## can be any vector in the ##xy## plane. Then no matter what ##\vec u## is ##\vec y = \vec u - \vec x## is a solution. So ##\vec u## and ##\vec x ## can be all over the place.LCSphysicist said:
Unless there was more info provided, I see no way to guess this 'solution' is what was wanted. Indeed, I would propose a better 'solution' is to omit ##\vec b## and define a as a unit vector. ##\frac{m\vec v}{|\vec v|^2}+\lambda\hat a##, where ##\vec v.\hat a=0##, generates all solutions of ##\vec x.\vec v=m##.LCSphysicist said: