# Thread: exterior algebra in R3

1. ## exterior algebra in R3

can anyone give me a hint on proving this,

dx^dy=dxdy
dy^dx=-dxdy

any words will be appreciated.

2. Originally Posted by enricfemi
can anyone give me a hint on proving this,

dx^dy=dxdy
dy^dx=-dxdy

any words will be appreciated.
A little more context would be helpful

P.S. Doesn't the second follow from the first since in any exterior algebra $\displaystyle u\wedge v=-(v\wedge u)$?

I rise this question while learning integration on manifolds, especially Stokes's theorem.

Does the dx^dy give the orientation of dxdy?
then what about dy^dx^dz=-dxdydz? why does the volume can have orientation?

Originally Posted by Drexel28
A little more context would be helpful

P.S. Doesn't the second follow from the first since in any exterior algebra $\displaystyle u\wedge v=-(v\wedge u)$?

4. forget anything like dxdy, just treat it as a short form of dx ^ dy.