摘   要：当前，将向量引入中学数学课程是世界性方向【1】。不同于我们以往所认识的标量，向量作为一个“矢量”在高中数学中登场，一直都是高中数学中一个比较基础的重要概念。向量本身既具有“数”特点的，又具有“形”的特点，较为直观的体现了“数形结合”这个重要的数学思想。正因为具有这样的特征，使得向量成为沟通代数与几何的桥梁之一。

本文将在阐述有关高中数学中向量的基本概念和运算法则的基础上，通过一些实际例题，对向量在高中数学尤其是代数中的实际应用进行较为全面细致的讨论，从而总结出向量在高中代数中的规律。讨论将采用分类的方式，如向量在求不等式、取值范围、解三角形等问题中的实际作用。

另外要注意的是，尽管向量在解题是具有一定的优势，但是我们仍需应该多角度地看待向量。世界上没有一种方法是万能的，向量也是如此。

At present, it is a worldwide direction to introduce vector into middle school mathematics curriculum.

Unlike the scalar we have known in the past, vector is a "vector" in high school mathematics, and it has always been an important concept in high school mathematics. The vector itself has the characteristics of "number" and "shape", which is more intuitively reflected in the important mathematical thought of "combination of numbers and shapes". Because of these characteristics, vectors become a bridge between algebra and geometry.

On the basis of explaining the basic concepts and algorithms of vector in high school mathematics, this paper will discuss the practical application of vector in high school mathematics, especially algebra through some practical examples, so as to sum up the rules of vector in high school algebra. The discussion will take the form of classification, such as the practical role of vectors in finding inequalities, ranges of values, and solving triangles.

Another thing to note is that although vectors have certain advantages in solving problems, we still need to look at vectors from different angles. No way in the world is omnipotent, so is vector.

关键词：向量法：数形结合；高中数学；代数问题； 

Keywords: Vector method ; Combination of numbers; High school mathematics; Algebraic problem;

目    录

引  言 4

1向量 4

1.1向量的概念 4

1.1.1向量 4

1.1.2向量的表示 4

1.1.3向量的模 4

1.1.4零向量 4

1.1.5单位向量 5

1.1.6相等向量 5

1.1.7共线向量（平行向量） 5

1.1.8向量的夹角 5

1.1.9平面向量基本定理 5

1.1.10共面向量 6

1.1.11空间向量基本定理 6

1.2向量的运算 7

1.2.1向量的加法 7

1.2.2向量的减法 8

1.2.3实数与向量的乘法 8

1.2.4向量与向量的乘法 8

1.2.5向量运算的坐标表示 9

2向量在高中代数中的应用