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向量在立体几何中占有重要的地位,且扮演着一个非常重要的角色,其应用打破了立体几何的传统解法,可以减少大量的辅助作图以及对图形的分析、想象过程,能直接使用代数运算来解决立体几何中的计算和证明问题.本文分类例析,供读者参考.一、利用向量处理垂直问题空间的线线、线面、面面垂直关系,都可以转化为空间内两个向量的垂直问题来解决.1.证明直线与直线垂直可以转化为证明这两条直线的方向向量垂直.2.证明直线与平面垂直可以转化为证明直线的方向向量与平面的法向量平行或证明直线的方向向
The vector occupies an important position in the three-dimensional geometry and plays a very important role. Its application breaks the traditional solution of the three-dimensional geometry, can reduce a large number of auxiliary mapping and analysis of graphics, imagination process, can directly use algebra To solve the problem of calculation and proof in the solid geometry.This paper classifies and analyzes for the reader’s reference.Firstly, using the vector to deal with the vertical line of the problem space, the line surface, the surface vertical relationship, can be transformed into two vector Vertical problem to solve.1 Prove that the straight line and the vertical line can be transformed into the vertical vector to prove that the two straight lines.2.Prove that the straight line and the plane vertical can be converted to prove that the straight line direction vector and the plane normal vector parallel or prove straight Direction to