Normal vector points up. Imagine that you put your thumb along c, your index towards s and then your middle finger points up.
法向量向上，想象你把你的大拇指沿着C放，食指指向s，那么你的中指就会向上。
In fact, our vector field and our normal vector are parallel to each other.
事实上，给定的向量场与法向量是相互平行的。
And, we know how to find a normal vector to this plane just by looking at the coefficients.
我们已经知道，如何根据系数找到这个平面的法向量。
This is a normal vector of the same length as n, well, up to sign.
这是与N长度相同的法向量，只是符号不定。
Well, to get our conventions straight, we should take the normal vector pointing up for compatibility with our choice.
为了配合约定习俗,选择相容的、指向上的法向量。
OK, and that's going to be the normal vector to the surface or to the tangent plane.
这就是切平面的，或者说这个曲面的法向量。
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。
K instead of using the vertical vector k, you use the normal vector I.
你用了法向量i，而不是竖直向量。
This vector is called a normal vector or normal for short.
这一向量就称为法线向量或简称为法线。
That is our convention to get a unit normal vector that points to the right of the curve as we move along the curve.
这是约定的得到单位法向量的方法，这种做法使得，当沿着曲线行进时，法向量始终指向右手方向。
The normal vector pointing up, here we know what it means.
法向量指向上，这里我们知道它是什么意思。
Well, you know the normal vector.
那么当然知道它的法向量。
That corresponds to normal vector pointing up.
那相当于法向量指向上。
那么法向量又是什么呢？
Tasklets from the high-priority vector are serviced first, followed by those on the normal vector.
来自高优先级矢量的微线程先得到服务，随后是来自正常优先级矢量的微线程。
Why else would you know a normal vector?
还有什么原因你会知道法向量？
The normal vector is just sticking straight up or straight down.
从而法向量的方向是竖直向上或向下的。
That means your normal vector points down.
那意味着法向量指向下。
Hopefully, you can see that if I take a normal vector to the sphere it is actually pointing radially out away from the origin.
我希望大家能够了解，如果我将法向量平移至球面，那么它将以原点为心向外放射。
Let me re-explain quickly how I got a normal vector for the cylinder.
我来再次解释一下如何得出这个圆柱面的法向量。
Now take your disk with its normal vector sticking up.
现在我们拿这个法向量向上的圆盘。
Why would we ever know a normal vector?
为什么我们会知道法向量？
The notation suggests it is a normal vector, so what does that mean?
从记号来看，是一个法向量，那它有什么意义呢？
But you can also just stay with a normal vector.
但是你也可以继续只用法向量的。
And then get this equation for the plane using the normal vector.
然后利用法向量得出切平面的方程。
Just to reiterate what I said, positively here means, because we are going counterclockwise, the normal vector points out of the region.
再说一遍，这里“正的”意味着…，由于是逆时针走向，法向量指向区域外侧的。
Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?
现在的问题是，曲面上这一小块儿的面积是什么，及其法向量是什么？
It can be a normal vector of any length you want to the surfaces.
它可以是曲面上想要的任意长度的法向量。
And that is, in general, not a unit normal vector.
这通常不是一个单位法向量。
What if I give you a really complicated curve and then you have trouble finding the normal vector?
如果给你的是，一条很复杂的曲线，而又找不到法向量？
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