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。

Let AB be perpendicular to CD.

设ab垂直于CD。

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。

The surface is perpendicular to gravity.

它们平面垂直于重力。

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。

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 force is always perpendicular to the direction of motion.

因为这个力总是垂直,于运动的方向。

In other words, it's perpendicular to the plane of the two vectors.

换句话说，它垂直于，两个向量所处的平面。

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？

I mean when I say up, of course it is still perpendicular to the surface.

当我说向上时，它当然仍是垂直曲面的。

And so the liquid will say "I'm going to be perpendicular to gravity."

此时液体会说，“我要与重力相垂直。”

Then you know that the gradient of g is perpendicular to the level surface.

那么就知道了g的梯度,是垂直等值面的。

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。

Now, there's two different possible directions that are perpendicular to a plane.

现在，垂直于同一个平面的，有两个方向。

Being perpendicular to the surface means that you are perpendicular to its tangent plane.

垂直于曲面也意味着垂直于它的切平面，垂直于曲面也意味着垂直于它的切平面。

And suppose I'm rotating it about an axis perpendicular to the blackboard through that point.

假设我将其绕着，通过这点垂直于黑板，的轴旋转。

Now, if it's perpendicular to the plane, then in that case, it's perpendicular to the blackboard.

如果它垂直于这个平面，在那个例子里，它垂直于黑板。

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。