向量法在中学数学解题中的应用摘要 向量在中学数学中占据着极大的比例，它也在历年高考题中频频出现，是架起代数、几何、三角函数之间的桥梁。因此，熟练地掌握向量知识并运用向量法来解决难题变得至关重要。本文从课程标准对向量的要求的认知出发，先查阅与向量发展有关的文献及资料，对向量学的发展历史进行总结并简单阐述，接着搜集与向量有关的高考题以及常见例题进行分析、钻研，从代数、平面几何、空间几何这三个方面考虑，对利用向量法证明等式与不等式问题、最值问题、立体几何中的平行于垂直关系、空间角的正、余弦值问题展开研究。不管在代数方面还是几何中，向量都能作为有力的解题工具，使求解的过程更简便、准确。在立体几何中，向量法的优点更加明显，既有利于培养空间思维能力与抽象能力，也提高了它在高中数学常用方法中的地位。关键词 向量法 中学数学 问题分析The application of vector method in mathematics problem solvingAbstract Vector occupies a large proportion in middle school mathematics, and it also appears frequently in the college entrance examination over the years. It is a bridge between algebra, geometry and trigonometric function. Therefore, it is very important to master vector knowledge and use vector method to solve the problem. Starting from the recognition of the requirements of the curriculum standard for vector, this paper first looks up the literature and materials related to the development of vector, summarizes and briefly expounds the development history of vector science, then we collect the college entrance examination questions related to vectors and common examples for analysis and research. From the three aspects of algebra, plane geometry and space geometry, we study the problems of proving equality and inequality, maximum value, parallel to vertical relationship in solid geometry, positive and cosine value of space angle by vector method. No matter in algebra or geometry, vector can be used as a powerful tool t...
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