在高中教材人教A版选修2-1的第三章中,有利用向量的方法解决立体几何的证明问题的内容,其中提到证明直线与平面平行等价于证明直线的方向向量与平面的法向量垂直.这个方法虽然可行,但是我通过学习实践发现,求一个面的法向量的运算量往往比较大.尤其是在不便于建立空间直角坐标系的情况下,这种方法更显得复杂和繁琐.然而,在立体几何中证明直线与平面平行一般属于较容 In the third chapter of high school textbook teaching A version of elective 2-1, the use of vector method to solve the problem of proof of three-dimensional geometry, which mentions that the proof of straight line and plane parallel to the equivalent of proof of the direction of the line vector and plane This method is feasible, but I found through practice that it is often more computationally intensive to find the normal vector of a surface, especially when it is inconvenient to construct a rectangular Cartesian coordinate system However, it is generally accepted in solid geometry that lines and planes are generally parallel