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法向量是研究二面角问题的一个有效工具,在应用中,学生常困惑于二面角大小与其两半平面法向量的夹角的关系是相等还是互补,原因在于难以准确判断法向量的方向.对于该问题,可以通过构造辅助向量,利用数量积与两向量夹角的关系来准确判断出两法向量的方向,从而有效地解决了学生的困惑.
Normal vector is an effective tool to study the problem of dihedral angle. In the application, students often confused whether the relationship between the dihedral angle and the angle between two half-plane normals is equal or complementary because it is difficult to judge the direction of the normal vector accurately For this problem, the auxiliary vector can be constructed and the relationship between the quantity product and the angle of two vectors can be used to judge the direction of the two normal vectors accurately, which can effectively solve the student ’s confusion.