在近期北京各区高三数学期末考试立体几何考题中,学生的得分情况并不理想。在解题中为避免难度较大的几何推理,学生常建立空间坐标系利用坐标形式的向量解决问题。而恰当利用非坐标形式的向量解题,既可以避开技巧要求过高、转化复杂的几何法,又可以很好地回避有时建系的困难。下面笔者从几道立体几何考题谈起,与读者交流。 In the recent Beijing high school mathematics final exam three-dimensional geometry test questions, the students score is not ideal. In solving the problem in order to avoid the more difficult geometric reasoning, students often establish space coordinate system using coordinate form of vector to solve the problem. Appropriate use of non-coordinate form of vector-based problem-solving, both to avoid the high skill requirements, the transformation of complex geometric method, but also can be very good to avoid the difficulty of sometimes building. The following author from a few road talk about three-dimensional geometry, and readers exchange.