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现代几何研究的一种重要思路是代数化,运用空间向量把空间图形的性质代数化,用运算推理代替几何推理,用向量代数的方法解决立体几何问题,可以减少添加辅助线的麻烦,避开了一些较复杂的空间想象,从而降低解题难度.若能结合空间向量的坐标运算进行定量计算,可以使问题更为简单.如果向量a的有向线段所在的直线垂直于平面α,则称向量a垂直于平面α,记作a⊥α,此时称向量a叫做平面α的法向量.教材中只给出了这个概念,并未对此做进一步研究.下面将平面法向量在立体几何中的应用作初步探讨.
An important idea of modern geometric research is algebraicization. The use of space vectors to algebraize the nature of spatial graphs, the use of computational reasoning instead of geometric reasoning, and vector algebra to solve the problem of solid geometry, can reduce the trouble of adding auxiliary lines, avoiding Some more complex spatial imaginings reduce the difficulty of solving problems. If we can combine the space vector’s coordinate calculations for quantitative calculations, we can make the problem simpler. If the straight line of the vector a’s directed line segment is perpendicular to the plane α, we say The vector a is perpendicular to the plane α and denoted by a⊥α. At this time, the vector a is called the normal vector of the plane α. This teaching material is only given this concept, and has not been further studied. The plane normal vector is used in the three-dimensional geometry. Application in the preliminary discussion.