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It comes from the fact that velocity is a vector and you can change your velocity vector by changing your direction.
其原理就是,速度是矢量,你可以通过改变方向来改变速度
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This formula doesn't tell you which way it's pointing, because it's a scaler; it's not a vector equation.
这个式子没有说明方向,因为这是一个标量而非矢量方程
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Once you've got that, you can do minus 7 times a vector Just take the vector, multiply it by Pi and flip it over.
明白这点之后,你就可以计算-7乘以矢量,只需用 π 去乘以那个矢量,然后将其方向调转
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We learned that a vector is a quantity that has a magnitude and a direction.
我们已经知道矢量是一个,既有大小又有方向的量
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It's good to have a vector pointing in the radial direction of length one.
所以引入这么一个模长为 1,方向沿圆心向外辐射的矢量作用很大
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So the minus vector is the same vector flipped over, pointing the opposite way.
因此负矢量即为同一矢量的翻转,指向相反的方向
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This is the reason behind saying a vector has a magnitude and a direction.
这就是矢量既有大小也有方向的原因
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The idea that he had was, if you go from me to you, with a clockwise rotation, you go from you to me by a counterclockwise rotation.
他的方法是这样的,如果这个矢量从这转到那是顺时针方向,那么这个矢量转回来就是逆时针方向
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The tangent's pointing towards the direction you are headed at that instant.
切线的方向就是,速度矢量在那个瞬时的指向
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Pick any two perpendicular directions Then the same entity, the same arrow which has an existence of its own, independent of axis, can be described by you and me using different numbers.
选取两个互相垂直的方向,这样同样的物体,同一矢量,并且是独立于坐标轴而存在的,可以被你和我用不同的数字来描述
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The fact that when you go in a circle, you accelerate is what we're learning here, coming from the fact that velocity is a vector and its change can be due to change in the magnitude or change in direction.
而当你做圆周运动时你也在加速,这是我们在这里所学到的,原因就在于,速度是一个矢量,其变化可以通过改变模长,或者方向来实现
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This vector i prime has got a horizontal part, This kind of trigonometry you should know all the time.
矢量 i' 有一个水平方向的分量,这类三角关系你们应该已经很熟悉了
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At each point, er is a different vector pointing in the radial direction of length one.
矢量 er 在每一点处都不同,方向都从圆心指向该点,模长为1
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er is a vector at each point of length one pointing radially away from the center.
r 是一个模长恒为 1 的矢量,方向沿半径向外
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And I can find the orientation of the arrow You have the option of either working with the two components of A or with the arrow.
我也可以求得矢量的方向,你可以选择使用,A 的两个分量或者矢量图来计算
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So i and j are vectors of length one, pointing along x and y.
和 j 是模长为1的矢量,分别指向 x 轴和 y 轴方向
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i and j are unit vectors in the x and y directions.
和 j 分别是 x 和 y 方向上的单位矢量
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Unit vector i points away from the origin in the x direction.
单位矢量 i 从原点指向 x 轴正方向
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If you say, "Add the vectors, " I would just add the x to the x and the y to the y and I'm keeping track of what the sum is.
如果你们说 " 将矢量相加 ",我就把同为 x 轴方向的分量相加,同为 y 轴方向的分量相加,然后就能得出这两个矢量的和是多少了
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If you want to add two vectors, you can add the arrows by the rule I gave you or just add the components of x of the two guys to get the component of the sum and likewise for the y.
如果要把两个矢量相加,你可以用我教给你们的箭头相接的方法,或者就将二者的 x 分量相加,得到和矢量的 x 分量,y 方向也是这样
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