浅析圆“包装”的平面向量最值问题

Analysis of Maximum or Minimum Value of Plane Vector for the Circular “Packing”

圆是几何的重要学习对象,向量是连接代数、几何、三角的桥梁。对于圆中出现的平面向量问题,求解过程中,可以以圆为辅助条件,根据向量运算求向量内积的最值;利用圆的几何性质求向量长度的最值;以圆为隐形存在,向量的运算和性质是主导,求条件最值;并探讨了求向量的夹角取值范围问题。

The circle is an important learning object of geometry while vector has dual identities of algebra and geometry,which performs the function of linking algebra,geometry and triangle as a bridge. This paper argues that in the solving process of plane vector problems in a circle,the circle can be taken as the auxiliary condition to evaluate the extreme value of inner product of vector according to vector operation,the extreme value of vector length can be evaluated by making use of geometric properties of the circle and the extreme value of condition can be evaluated by taking circle as stealthy existence,vector operation and properties as leading elements. Besides,it discusses the value range of angle for vector solving.