Are the lines perpendicular to each other?
这些直线相互垂直吗？
The left wing dipped until it was perpendicular to the ground.
左翼下垂至与地面成90度角。
When a surface is perpendicular to the rays, their intensity is at its maximum.
当表面与射线垂直时，射线的强度最大。
So, it's perpendicular to my curve.
它垂直于曲线。
should be perpendicular to the level set.
必须与水平集垂直。
And the force is perpendicular to the arm.
力是垂直于杆。
So it's still perpendicular to the same plane.
所以这个外积还是垂直于同一个平面。
And it will still be perpendicular to the curves.
它还是垂直于那些曲线。
Well, it's the direction that's perpendicular to this plane.
它其实是朝垂直于平面的方向。
You might be able to draw curves that are perpendicular to it.
或许你可以画出每点都垂直于向量场的曲线。
The gradient vector would be going perpendicular to the level.
梯度向量应该垂直于等值线。
And then there is the normal force perpendicular to the surface.
这个力，垂直于斜面。
And these forces are both perpendicular to the displacement.
这些力都在位移的垂直方向上。
So, how do we find this vector that's perpendicular to the plane?
所以，我们要怎么找，垂直于这个平面的向量？
The lighter should sit perpendicular to the neck of the bottle.
打火机应该与瓶颈垂直。
And so it was rotating like this and was perpendicular to the disk.
它这样旋转，垂直于圆盘。
We have seen that the gradient is perpendicular to the level surface.
我们已经知道，梯度是垂直于等值面的。
Do you mean how do I know that it is perpendicular to a level curve?
你想问的是，我如何知道它是和等高线垂直的吗？
That means that the gradient of f is perpendicular to the level set of g.
也就是说f的梯度向量,应该与g的水平集垂直。
And I will call this direction y, as I always do perpendicular to the surface.
照惯例把垂直方向，设为y方向。
The directional derivative in a direction that's perpendicular to the gradient is basically zero.
垂直于梯度的方向上,方向导数为零。
Why is that? Well, let's say that we know how to find a vector that's perpendicular to our plane.
为啥呢？呃，就是说，我们知道，怎么画垂直于这个平面的向量。
So, see, this coefficient becomes zero exactly when the line is perpendicular to the normal vector.
看到了吧，系数变为0了，当直线垂直于法向量的时候。
On a snowboard, the torso's natural position is more or less perpendicular to the direction of motion.
在单板上，人的躯干大致和运动方向垂直，十分自然。
That means a vector that is at every point of the curve perpendicular to the curve and has length one.
也就是，曲线每一点上,垂直于曲线，模长为1的向量。
But we know another vector that is also perpendicular to the level set of g. That is the gradient of g.
但我们知道有另外一个向量也是和g的等值面垂直的，这个向量就是g的梯度。
Consider a ball that is spinning about an axis perpendicular to the flow of air across it (see left).
观察一个旋转轴与空气流动方向垂直的足球(见上图)。
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