# Math Help - odd verctor problem

1. ## odd verctor problem

a,b,c,d,e and f are all verctors
proof: (a×b,c×d,e×f)=(a,b,d)·(c,e,f)-(a,b,c)·(d,e,f)
ps:It rather confuses me that the verctors are restricted in parentheses oderly.I will appreciate it if you show the meaning of this.

2. ## Re: odd verctor problem

Hey CosmoBlazer.

I agree that the notation is confusing. Can you possibly show us where you got the definition from? Also you might want to check if its a scalar triple product:

Triple product - Wikipedia, the free encyclopedia

3. ## Re: odd verctor problem

What does "(a×b,c×d,e×f)" mean? axb etc are vectors. What does a triple of vectors mean? What does "(a,b,d)·(c,e,f)-(a,b,c)·(d,e,f)" mean? If "(a, b, c)" is the triple product of vectors as chiro suggests is the " $\cdot$" just multiplication of numbers?

4. ## Re: odd verctor problem

I believe (a,b,c) is a.bxc, a scalar. Then try to prove eq in post 1. If you can, it is.

5. ## Re: odd verctor problem

To start off the proof, note:
(a,b,c)=a.bxc
ax(bxc)=(a.c)b-(a.b)c
(axb).(cxd)=(b.d)(a.c)-(b.c)(a.d)
which come from vector algebra texts.

Then apply to post 1
(axb,cxd,exf) = axb.(cxdxexf)
cxdxe=(c.e)d-(c.d)e
cxdxexf=(c.e)dxf-(c.d)exf
(..)=(c.e)axb.dxf-(c.d)axb.exf

and continue on as a good excersize. let us know how you make out.