I have a basic wedge product question, I'm very new to this and have been looking at examples but still have trouble computing the following. If $u=(a_1,a_2,a_3,a_4)$ and $v=(b_1,b_2,b_3,b_4)$ and $w=(c_1,c_2,c_3,c_4)$, compute $dx_1 \wedge dx_2 \wedge dx_3 (u,v,w)$.
I have no clue where to begin. I can find $dx_1 \wedge dx_2(u,v)=(a_1b_2-a_2b_1)$ but how to continu from there?
Help would be much appreciated.