# Regular hexagon sides as vectors

So I'm having this problem (linear algebra).

Given that vector a is defined as OA, and b as OB. I need to express other ones in function of those ones.

I currently found that BA is b-a and DE is -a+b and also that OD is -a and DA is 2a. All using the definition of vectors. (I'm studying using Fraleigh's linear algebra.

But, the problem arise when trying to express BC cause I don't realize how. I now that since this is a regular hexagon the norm'll be the same as the BA and actually the other sides but can't express in terms of a and b.

Any help? Thanks.

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Remember that a vector has magnitude and direction, but not a fixed starting point. So with attention to sign you might look at a parallel vector you do know and work from there. – Mark Bennet Aug 24 '11 at 15:20
Thanks mark (didn't realize that of not starting point), so it'll be the same as -a? – Randolf Rincón Fadul Aug 24 '11 at 15:23
Glad the hint helped! – Mark Bennet Aug 24 '11 at 19:51

Note that DO, OA, CB, EF are all the same vector $a$, but just moved across the plane. Similarly DE, CO, OF, BA are the same and are all $b-a$ ($b-a$ and $-a+b$, which you give for BA and DE, are of course the same), and DC, EO, OB and FA are all the same vector and are all $b$. And in particular, BC is -CB, so it is $-a$.

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Thank you very much t-laarhoven. For the detailed explanation :) – Randolf Rincón Fadul Aug 24 '11 at 15:28