1. The problem statement, all variables and given/known data Find nonzero scalars a, b, c, such that au+b(u-v)+c(u+v)=0 for every pair of vectors u and v This isn't a homework question, more of a conceptual exercise, but I want to understand it thoroughly. 3. The attempt at a solution I've gone to u(a+b+c) + v(c-b)=0 then I couldn't quite figure where to go next. There is so many unknowns at once it's a little disorienting where to start first. Then I figured to try splitting it into the vector pairs, a(u1,u2)+b(u1-v1, u2-v2)+c(u1+v1, u2+v2)=0 but I am still stumped as to where to go from here. It seems like it's painfully simple but I'm not quite seeing it. EDIT1: I've attempted putting the vectors in a system of equations; u1a+u1b+u1c-v1b+v1c=0 u2a+u2b+u2c-v2b+v2c=0 but once again I hit a dead end and only get the scalars equaling zero.