例如，在某些情况下，如果已知向量场与曲线相切，或者内积是一个常数等等，那么结果将会很简单。

And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.

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这门课我们首先学习的概念是向量，以及怎样做向量的内积。

So, the first things that we learned about in this class were vectors, and how to do dot-product of vectors.

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本文通过构造向量，将向量的内积的性质运用于不等式的证明中，使得一些不等式的证明更加简捷。

A property of inner product is used for proving inequalities by constructing some spacial vectors, it can simplify the processes of the proof.

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