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纵观历年高考数学试卷,立体几何是必考的题型,其考查的立足点往往放在空间图形上,突出对空间观念和空间想象能力的考查,注重空间中对点、线、面的各种关系的研究。由于向量只与其方向和大小(长度)有关,具备了代数与几何的双重身份,在解决几何问题时,恰当地运用向量方法,就能做到几何问题代数化,更有利于问题的解决。针对近年来的高考命题侧重于考查直线与直线、直线与平面、平面与平面的各种位置关系及又易于建立空间直角坐标系的题型特点,本文就如何运用向量方法破解立体几何题谨提出浅见。
Throughout the college entrance examination mathematics papers over the years, the three-dimensional geometry is the type of test will be the basis of its test often placed on the space graphics, highlighting the space concept and spatial imagination of the test, focusing on the space point, line, surface Research on the relationship between species. Because vector is only related to its direction and size (length), it has the dual identities of algebra and geometry. When solving the geometric problem, the proper use of vector method can do the geometric problem algebra, which is more conducive to the solution of the problem. In view of the college entrance examination proposition in recent years focused on examining the linear and linear, linear and plane, the plane and the plane of the various positional relationships and easy to establish space rectangular coordinate system question characteristics, this paper on how to use vector method to solve the problem of solid geometry humble opinion.