Proof for cross product a x b= -b x a

[senorclean]

This problem involves vectors and it's a fairly basic proof but I can't seem to wrap my head around it.

I tried to just separate the vectors into their components and cross them but then I just get another set of coordinates that doesn't seem factorable. I really can't see any way to manipulate it.

I thought about just doing the cross product of -(b x a) and showing that the coordinates would be the negative version of a x b but I'm not sure if that's even proving anything. I hate proofs. Any guidance would be greatly appreciated.

 

[╔(σ_σ)╝]

Yes,doing the cross product of a x b and showing it is equal (component wise) to -b x a is enough.

 

[senorclean]

ok then. gracias