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在早先的视频里，我们介绍过

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如何用长度和方向

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来完全定义一个向量，两者缺一不可。

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在这里有一个已经被这样定义的向量。

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我们已知它的长度

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等于3个单位长度。

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这两边的平行线，

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看上去像双重绝对值的符号，

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代表向量a的长度。

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这个式子相当于指定了

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图中箭头的长度为3个单位长度。

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与此同时我们还规定了它的方向。

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如图所示，这个向量的方向是

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相对正东方向逆时针旋转30°。

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在本视频中，我们将会介绍

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定义该向量的另一种方法。

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这是一种通过分量来定义向量的方法。

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我们将关注

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这个向量的尾巴

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和头部，

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考虑从它的尾巴走到头部，

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横坐标x改变了多少？

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我们可以看出，x的变化量

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等于这条红线的长度。

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我们的横坐标从这个值变成了这个值。

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我们还要考虑纵坐标y的变化。

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假如我们从此处向上走到这里，

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y方向的变化量就对应这条紫线的长度。

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让我们给它们做上标记。

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x的变化量记作Δx，y的变化量记作Δy。

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请设想一下，

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假如有人告诉了你Δx和Δy，

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你应该可以相应重建出这个向量：

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从这里出发，先改变x，

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再改变y，得到向量的头部

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相对尾部的位置。

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我们相应将上述定义记作：

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向量a，等于，写上两个括号，

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在括号中填入Δx，逗号，Δy。

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对图中的这个向量而言，

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更具体地说，

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我们已知它的长度为3。

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它的长度为3。

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我们还知道这条线处于水平方向，

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而这条线处于竖直方向。

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此处是一个直角。

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于是我们可以使用以往的几何知识。

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别担心，有必要的话你可以复习一下。

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我们可以使用一点几何，

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或者三角学知识：

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我们已知这个角的大小，

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以及斜边的长度，那么与30°角

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相对的边的长度就等于斜边的一半，

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也就是3/2。

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