a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?

- Aug 31st 2012, 12:03 AMTaTzRE66a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?
a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?

- Sep 1st 2012, 08:14 AMawkwardRe: a,b,c are vectors. How to prove vector b = c, given a.b = a.c and axb = axc?
I think we need an additional assumption that ; otherwise the claim is not true.

So assuming , as a first step let's see if we can show that if and then .

We have

so

, hence .

Finally, to show that if and then , let above.