The actual 3D cross product takes in two vectors and spits out a vector.

实际的三维外积是两个向量 然后得到一个向量。

But this idea actually gets us really close to what the real cross product is.

但是这个想法实际上让我们非常接近真正的叉乘。

So that performing the linear transformation is the same as taking a dot product with that vector the cross product.

所以进行线性变换就等于对这个向量做点积也就是叉乘。

Here, I'll try to hit the main points that students are usually shown about the cross product.

在这里 我将试着抓住学生们通常学到的关于叉乘的要点。

Of course, you all know that this is not the 3D cross product.

当然 你们都知道这不是三维叉乘。

This is the fundamental reason why the computation and the geometric interpretation of the cross product are related.

这就是为什么叉乘的计算和几何解释是相关的根本原因。

So that wraps up dot products and cross products.

这就包含了点积和叉乘。

The cross product of VNW, written with the X shaped multiplication symbol, is the area of this parallelogram.

VNW的叉乘 用X形乘法符号表示 就是这个平行四边形的面积。

The important part here is to know what that cross product vector geometrically represents.

这里重要的部分是知道叉乘向量在几何上表示什么。

So to back up a bit, remember in two dimensions what it meant to compute the two D version of the cross product.

回想一下 在二维空间中 计算二维空间的外积意味着什么。