If you swapped V-N-W, instead taking W, cross V, the cross product would become the negative of whatever it was before.

如果交换V-n-W 而是用W叉乘V 叉乘就变成了之前的负数。

Then when we associate that transformation with its dual vector in three D space, that dual vector is going to be the cross product of V-N-W.

然后当我们把这个变换和它在三维空间中的对偶向量联系起来 这个对偶向量就是V-N-W的外积。

What I'm going to do is define a certain linear transformation from three dimensions to the number line, and it'll be defined in terms of the two vectors V-N-W.

我要做的是定义一个从三维到数轴的线性变换 它由两个向量V-N-W定义。