用空间向量解决立体几何的平行或共面、垂直、空 间角和空间距离等问题,同学们往往习惯于建立空间直 角坐标系,然后运用向量的坐标运算,实现从已知向求 解转化.其实,选择向量的基底,运用向量代数运算,并 依据有关性质和定理向求解转化.这也是解决立体几何 问题的基本思路、方法. 一 垂直问题 例1 如图1,在正方体ABCD-A1B1C1D1中,O为 AC与BD的交点,G为CC1的中点.求证:A1O⊥平面 GBD. Using space vectors to solve the problems of parallel or coplanarity, verticality, spatial angles, and spatial distances of three-dimensional geometry, students are often used to establish a space rectangular coordinate system, and then use vector coordinate operations to convert from known to solving. In fact, Select vector basis, use vector algebra operations, and based on the properties and theorems to solve the transformation. This is also the basic ideas and methods to solve the problem of three-dimensional geometry. A vertical problem Example 1 In Figure 1, in the cube ABCD-A1B1C1D1, O is The intersection of AC and BD, G is the midpoint of CC1. Proof: A1O plane GBD.