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立体几何引入空间向量后,可以借助向量工具,使几何问题代数化,降低思维难度,尤其是在探索空间点的位置时,更可以发挥这一优势,以下举例说明.例1(2004年湖北省高考题)如图1,在棱长为1的正方体ABCD-A1B1C1D1中,点E是棱BC的中点,点F是棱CD上动点,试确定点F的位置,使得D1E⊥面AB1F.
After the spatial vector is introduced into the three-dimensional geometry, the vector tool can be used to make the geometric problem algebraic and reduce the difficulty of thinking. Especially when exploring the position of the spatial point, this advantage can be further exerted. The following example is illustrated. Example 1 (2004 Hubei Province College entrance examination questions) as shown in Figure 1, in the cube with an edge length of 1 ABCD-A1B1C1D1, point E is the midpoint of the edge BC, point F is the moving point on the edge CD, try to determine the position of the point F, so that the D1E surface AB1F.