Well, you know the normal vector.
那么当然知道它的法向量。
那么法向量又是什么呢？
Why would we ever know a normal vector?
为什么我们会知道法向量？
Why else would you know a normal vector?
还有什么原因你会知道法向量？
That means your normal vector points down.
那意味着法向量指向下。
The normal vector will just be the gradient.
法向量就是梯度向量。
That corresponds to normal vector pointing up.
那相当于法向量指向上。
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 that is, in general, not a unit normal vector.
这通常不是一个单位法向量。
Now, let's multiply that by the unit normal vector.
现在用单位法向量乘以那个。
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。
All right, it has the same normal vector as the surface.
它和曲面有相同的法向量。
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。
And so the normal vector is going towardS what is up for me.
所以法向量指向我的上方。
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。
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。
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 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。
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。
First of all, what does the normal vector to a cylinder look like?
先思考一下圆柱面的法向量？
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？
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。
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。
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。
So, for a sphere, the normal vector is divided by the radius of the sphere.
关于球体，法向量是,除以球的半径。
And let's say I want to Orient my cylinder so that the normal vector sticks out.
我给这个圆柱确定了方向，即法向量指向圆柱之外。
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。
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。
You can just multiply a normal vector by any constant, you will still get the normal vector.
一个法向量与任意常数相乘，还是法向量。
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