向量具有实数运算的某些性质,又具有形的直观感知功能,是数形结合的良好载体,在一些求向量模的值或范围的题目中,固然可用向量数量积运算,但运算量大且杂,不具有直观性,有时很难精确表达范围,若巧借题设条件,利用辅助圆,能直观地知道向量模的变化趋势,减少运算量,但对圆的知识提出了更高要求.兹举数例,供读者参考. Vector has some properties of real number operation, but also has a shape of intuitive perception, is a good carrier of the combination of numbers, in some questions or range of vector mode, although the number of vectors available vector operation, but a large amount of computation Miscellaneous, not intuitive, and sometimes it is difficult to accurately express the range, if the Qiao by setting the conditions, the use of auxiliary circle, can intuitively know the trend of vector mode, reduce the amount of computation, but put forward higher requirements for the circle. I give a few examples, for readers reference.