如果有两个矢量。
And, we don't really need vectors.
当然我们可以不用向量。
I don't write them down as vectors.
我没写成矢量。
两个向量的点乘积。
We use boldface type for vectors.
我们用黑体形式表示矢量。
Returns true if vectors different.
如果向量不同将返回真。
Returns true if the vectors are equal.
如果两个向量相等，返回真。
Then you have two vectors given on the plane.
然后得到平面上的两个给定向量。
How do we decide if two vectors are parallel?
我们平时怎么验证两个向量平行呢？
To see a simple example, let us create two vectors.
为了查看一个小例子，让我们来创建两个向量。
Retrovirus is one of the vectors in common use.
逆转录病毒是最为常用的载体之一。
The two vectors are proportional by a factor of two.
这两个向量也是相差1倍。
Any plane actually has infinitely many normal vectors.
每一个平面都有无数条法向量。
Now we have to find three vectors which we don't know.
现在我们找到了三个不知道向量。
There are also vectors, but I won't discuss them here.
也有向量，不过在这里不作讨论。
If the two vectors are the same length, it is easy.
如果两个向量的长度是相同的，它很容易。
So these six are numbers and these are the unit vectors.
这就得到6个数字,和3个单位矢量。
OK, more questions? So, what else can we do with vectors?
还有问题么？，好，那么我们还能对向量干什么呢？
Will we have to know how to rotate vectors and so on?
我们需不需要掌握如何旋转向量这些知识点？
This is a property of orthogonal vectors of length 1.
这是长度为1的正交向量的性质。
Now suppose, you would like to add two vectors together.
现在假设，你想补充两个向量在一起。
The second number is the number of constant vectors to load.
第二个参数指的是加载的常量向量的数量。
When I am at a minimum, the two gradient vectors are parallel.
当在最小值点的时候，两个梯度向量就垂直了。
V the weight, w, and v, these are the two vectors we've seen here.
重量是w和价值，这是我们看过的向量的两个值。
Time Gate Vectors are not the only means to access other realities.
时间门之多向矢量并不只是唯一通往其他实相的方式。
Nanoparticle has been the focus in recent research of vectors.
纳米粒是近年来载体研究中的热点。
And Y are vectors of the same size or matrices of the same size.
和Y是向量的大小相同或矩阵的大小相同。
we want to know what combination of those 3 vectors produce that one.
我们想要知道那三个向量的什么组合会产生那个。
Yet since then, more potential attack vectors have been revealed.
然而，也就是从那时起更多的潜在的攻击媒介显露出来了。
Yet since then, more potential attack vectors have been revealed.
然而，也就是从那时起更多的潜在的攻击媒介显露出来了。
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