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Initially I set u=(-1)(v+w), v=(-1)(u+w), w=(-1)(u+v) and then try to just insert those vectors into the thing I'm supposed to show; I don't know how to go from where I am though.
Currently at vxu+vxw+wxu
Quite certain you're supposed to use the fact that some of the vector products are orthogonal to each other and therefore 0
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Just arrived at wxu; still haven't shown for vxw though, it seems very chaotic just inserting relations over and over, is there a better way?
So say we have
SO I guess you could use this to show wxu by writing what I just wrote but your ui's as wi's and your vi's as ui's.
(Then do the same for vxw)
But this seams pretty long to me.
I will have to see if I can find a shorter way.
You would write your ui's as wi's by using ui+vi+wi=0 as ui=-(wi+vi)
Indeed, that's what I went for, managed to show that the left term was the right term; never got to the middle one though.
It seems like a mess using the laws though.
Hey! We use some cool properties!? :)
Like can we use ax(b+c)=(axb)+(axc)
This would cut out a lot of time.
This would make the proof like 100 times easier.
Because since w=-(u+v), then w=-u+(-v)
=vx(-u) + vx(-v)
Then we can also use -bxa=axb
and use axa=0