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.
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.
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.
数学上存在各种不同的抽象空间，例如向量空间，内积空间等。
There are many different types of abstract space in mathematics, for examples, vector space, inner product space, etc.
然后由平埘的点法式方程自然地引出了用坐标法定义向量的内积外积。
Then, we prove that the definition of coordinate method and that of vector method are equivalent.
在模糊内积空间的极小化向量定理基础上，给出了向量拟模糊正交定义，并在模糊内积空间中证明了投影定理。
Based on the minimizing vector theorem of the fuzzy inner product space, the pseudo fuzzy orthogonal vector is defined and the projected theorem of the fuzzy inner product space is testified.
构造向量，利用向量内积进行求解，为函数最值问题的解决，开辟了一种新的思路和方法。
But the author explored a new way to solve this problem, which is to wake up vector and make us of the internal product to go on solution.
第一章是向量代数，主要介绍向量的线性运算、向量的内积、向量的外积、向量的混合积和双重外积。
The first chapter is about vector algebra, introduces the vector of linear operations, inner product of vectors, vector outer product, vector product and double mixed exterior product.
另一类特征点是由法向量和视线向量的内积决定的，内积小于给定阈值的点称为特征点。
The other kind of feature points are those where the absolute value of the scalar product of its normal vector and the view vector is less than a threshold.
Drawa UMLdiagram first编写和测试vector2d定义加法，减法，数量积，输入和输出操作符一类，和两个二维向量的内积。
Write and test a class Vector2D to define operators for addition, subtraction, scalar product, input and output, and inner product of two 2d vectors.
Drawa UMLdiagram first编写和测试vector2d定义加法，减法，数量积，输入和输出操作符一类，和两个二维向量的内积。
Write and test a class Vector2D to define operators for addition, subtraction, scalar product, input and output, and inner product of two 2d vectors.
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