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平行与垂直是立体几何中重要的位置关系,是研究空间几何体位置关系的基础,是高考考查的重点。提起平行与垂直的证明,我们很自然地想到几何法或坐标形式的空间向量法。然而,在近几年高考中,证明平行与垂直关系的得分率并不理想,究其原因,几何法需要有很好的空间想像能力和几何推理能力,采取坐标形式的向量法,有时建立坐标系要通过一定的转化、证明,难度较大。一味强调坐标法和几何法会造成高考的失分,不妨运用非坐标形式的向量,也许会柳暗花明,别有洞天。
Parallel and vertical are three-dimensional geometry of the important positional relationship is the basis for the study of the spatial geometry of the location, is the focus of college entrance examination. With parallel and vertical proofs, it is natural for us to think of geometrical or coordinate space vector methods. However, in the college entrance examination in recent years, the proves that the scoring rate of parallel and vertical relationship is not ideal, the reason, the geometry method needs good spatial imagination and geometric reasoning ability, take the coordinate form of the vector method, and sometimes establish coordinates To pass a certain transformation, to prove that more difficult. Simply emphasize the coordinate method and the geometric method will result in the college entrance examination of the points, may wish to use non-coordinate form of the vector, may be superficial, there are unexpected.