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向量是数形结合的一个典范,更是解决问题的重要工具和方法,向量的模就是线段的长度,是一个实数;向量的点乘和向量的平方也是一个实数,巧妙利用向量与实数间的转换去解题,有时会起到意想不到的神奇效果,本文从解题的角度来说明向量与模相互转换的意义。
Vectors are a paradigm for the combination of numbers and shapes. They are also important tools and methods for solving problems. The modulus of a vector is the length of a line segment and is a real number; the dot multiplication of vectors and the square of a vector are also real numbers, and the vector and real numbers are used skillfully. Converting to solve problems sometimes has unexpected and magical effects. This paper explains the meaning of the transformation between vectors and modules from the perspective of problem solving.