来自《耶鲁大学开放课程：基础物理 第2集 第2集》

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  But you can also do something without drawing any pictures.
  但你不画图也可以做
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  That would come by saying,
  那就这样做
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  and I'm trying to add all these guys.
  然后把它们都加起来
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  But then, I combine i times Ax with i times Bx,
  然后我把 i ? Ax 和 i ? Bx 加起来
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  because that's the vector parallel to i, with the length Ax.
  因为这是平行于 i 模长为 Ax 的矢量
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  That's the vector parallel to i, with length Bx.
  这个是平行于 i 模长为 Bx 的矢量
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  That's clear. If I add them,
  这很明显 如果把他们加起来
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  I'll get a vector parallel to i with lengths Ax + Bx.
  就得到一个平行于 i 模长为 Ax + Bx 的矢量
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  Then j with Ay + By.
  同样有平行于 j 模长为 Ay + By 的矢量
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  I have to be really careful when I said, "Add the lengths."
  当我说"模长相加"的时候需要非常小心
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  I'm assuming all the components are positive.
  我现在已经假设所有值都是正的
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  If the Ax and Ay, some are positive and some are negative,
  如果 Ax 和 Ay 有正有负