(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Introduction to Vector calculations (Calculus 3)

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