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我们在解决立体几何问题时,有时若能合理地建立空间直角坐标系,利用向量法解题,要比用一般常规的逻辑推理、证明容易得多。原因是把抽象的推理问题转化成直观的计算问题来解决。尤其用“向量的数量积为零”来证明线线垂直:用“平面的法向量”解决有关角的问题时,显得格外简单。如在2006年全国普通高校招生统一考试中理科(19)题,文科(20)题:如图ll、l2是互相垂直的异面直线,MN是它们的公垂线段,若A、B在l1上,C在l2上,AM=MB=MN
When we solve the problem of three-dimensional geometry, sometimes it is easier to establish a space rectangular coordinate system and solve a problem by using the vector method than using the conventional logical reasoning and proof. The reason is to solve the problem of abstract reasoning by transforming it into an intuitive calculation problem. In particular, the “scalar product of the vectors is zero” is used to prove that the line is vertical: When using the “normal vector of the plane” to solve the problem of the relevant angle, it is particularly simple. For example, in the 2006 Unified Examination of National Universities for Enrollment, Science (19) title, liberal arts (20) title: Figure ll, l2 are mutually perpendicular straight lines, MN is their vertical line, if A, B in l1 On C, on l2, AM=MB=MN