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向量是高中数学教材重要内容之一,它融数与形于一体,既有代数的抽象性,又有几何的直观性。向量应用于代数中的一些不等式的证明,三角函数问题,几何尤其是立体几何问题中,使得需要苦思冥想的技巧显得不再那么重要。掌握向量这超强有力的工具,就可以实现抽象思维和形象思维的有机统一。本文通过运用向量来解决一些数学问题,与用传统的思路解决相比较,体现了向量解法的严谨的思维逻辑、化繁为简等优越性。向量法解决问题的过程中,体现出严谨的数形结合的思想,使问题的解决既简洁又显得顺其自然,尤其在立体几何问题上,一些为作辅助线而遇到的麻烦可以避免了,并且可以培养学生的严谨的逻辑思维能力。
Vector is one of the most important content of high school mathematics textbooks. It melts the number and form into one, has the abstraction of both algebra and the geometric intuition. The application of vectors to the identification of some inequalities in algebra, trigonometric functions, geometry, and especially to the problem of solid geometry makes the trickery of meditating less relevant. Master the vector of this powerful tool, you can achieve the abstract thinking and image of the organic unity of thinking. In this paper, we solve some mathematical problems by using vector, and compare with the traditional way of thinking, which reflects the rigorous thinking logic of vector method and the advantages of simplification and simplification. In the course of problem solving, the method of rigorously combining numbers and figures shows that the solution of the problem is both concise and natural. Especially in the case of the three-dimensional geometry, some troubles that are encountered as auxiliary lines can be avoided , And can develop students’ rigorous logical thinking ability.