这就是点积。
两个向量的点乘积。
Let us take a down-to-earth example of a dot product.
举一个点积的，现实例子。
There is another way that you can find the dot product.
另一个定义,点积的方法。
We can just find the angle using dot product So, how would we do that?
可以直接用点积来,找到这个角的大小，那么，怎么找呢？
The Vector Product node computes the Dot Product of two vectors.
矢量积节点计算两个向量的数目积。
So, product rule is OK for taking the derivative of a dot product.
那么乘积法则对点乘求导没问题。
I'm going to teach you — - just like with the dot product — two methods.
跟点积一样-，我会教你们-，两种方法。
The entries in the matrix product are obtained by taking dot products.
矩阵乘积里的元素是通过点乘得到的。
The dot product and matrices. Read Chapter3 through3.7 and do exercises.
点积和矩阵。阅读第三章至3.7以及做练习题。
The dot product of a pseudovector and a vector is called a pseudoscalar.
一个赝矢量和一个矢量的标识称为赝标量。
The dot product of a pseudo vector and a vector is called a pseudoscalar.
一个赝矢量和一个矢量的标识称为赝标量。
These two vectors are perpendicular exactly when their dot product is zero.
当点乘的数量积为零时,这两个向量垂直。
The dot product and matrices. Read Chapter 3 through 3.7 and do exercises.
内积和矩阵。阅读第三章至3.7以及做练习题。
It's the dot product between the normal vector of a plane and the vector along the line.
这是平面法向量，和沿直线向量的点积。
Now comes my method number two as we had with the dot product, is a geometrical method.
下面是方法,像点乘中一样，是个几何方法。
But now the power that I have to generate is the dot product between the force and the velocity.
但现在我要产生的，功率是力和速度，间的标量积。
OK, so now if we have a dot product that's zero, that tells us that these two guys are perpendicular.
所以我们现在有了一个点积为，这告诉我们两者是垂直的。
Well, we've learned how to detect whether two vectors are perpendicular to each other using dot product.
呃，我们学过怎么用点乘,来判断两个向量是否垂直。
Once you have such a formula, you do the dot product with this vector field, which is not the same as that one.
一旦你得到一个这样的计算式，你对向量场做点积，这和前面这个不一样。
There are two ways that we multiply vectors and one is called the "dot product" often also called the scalar product.
矢量乘法有两种,一种叫做“点积“,通常也被叫作“数量积
And I can rewrite this in vector form as the gradient dot product the amount by which the position vector has changed.
可以把这些用向量形式重新写下来，就是梯度向量和位置改变量的点积。
What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.
我们要做的是，沿着曲线的每一点上，取向量场和法向量的点积。
If you do the dot product with i hat, you will get the first component 0 that will be x1. One times x1 plus zero, zero.
如果你用i做点乘，你能得到第一个分量,那就是x1，1*x1+0
And, if you want to find what goes in a given slot here, then you just look to its left and you look above it, and you do the dot product between these guys.
如果你要找到，这个位置的数是什么，那你就往左，和往上看，然后用它们做点乘。
After the formula of documents are used to rewrite elements of Jacobian matrix, the vector cross product is changed into the vector dot product in Jacobian matrix.
利用现有的公式对雅可比矩阵中的元素进行改写，将矢量叉乘变为矢量点乘。
The core content of the theory is the correspondence between the thermal performance and the integral of the dot product of the velocity and the temperature gradient.
此理论的核心内容是传热率和速度矢量与温度梯度的点积值的对应关系。
OK, now, so there's an interesting thing to note, which is that we can use the usual product rule for derivatives with vector expressions, with dot products or cross products.
还有个很有趣的现象要注意一下，就是我们可以用乘积法则,对向量表达式求导，无论是点乘或叉乘。
This expression not only contains the term of dot product of velocity vector and temperature gradient, but also contains the dot product of velocity vector and the pressure gradient.
该式不仅含速度矢量与温度梯度矢量的点积项，还含有速度矢量与压力梯度矢量的点积项。
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