Right after they said it was a crime scene, you literally saw half of Laramie police spanning out through the dorms.

在他们说这是一个犯罪现场之后，你真的可以看到一半的拉勒米警察穿过宿舍。

We'll start in two dimensions. If you have two vectors V and W, think about the parallelogram that they span out.

我们从二维开始 如果有两个向量V和W 想想它们张成的平行四边形。

The unmanned Russian spaceship that span out of control while delivering cargo to the International Space Station last week is due to burn up in the atmosphere shortly.

上周俄罗斯无人飞船在向国际空间站运送物资时失控，而它原本是应该很快在大气中燃烧掉的。

This gives us the area of a parallelogram spanned out by those two vectors, with the possibility of being negative depending on the orientation of the vectors.

这就得到了由这两个向量张成的平行四边形的面积 根据向量的方向有可能是负的。

But thinking geometrically, we can deduce that this dual vector must be perpendicular to VMW with a length equal to the area of the parallelogram spanned out by those two vectors.

但从几何角度考虑 我们可以推导出这个对偶向量必须垂直于VMW 其长度等于由这两个向量张成的平行四边形的面积。

But the important part here is that it stays on the line, that it spans out without getting rotated off of it, for a glimpse of why this might be a useful thing to think about, consider some three dimensional rotation.

但这里重要的部分是它保持在直线上 它张成空间而没有旋转 为了让我们了解为什么这可能是一个有用的东西 考虑一些三维旋转。

And as you know from Chapter five, geometrically, this would give you the volume of a parallellapiped spanned out by those three vectors, with a plus or min assigned depending on the right hand rule orientation of those three vectors.

在第五章中 从几何上讲 这就得到了由这三个向量张成的平行四边形的体积 加号或最小值取决于这三个向量的右手定则方向。