一道空间解析几何问题的八种解法

Eight Approaches to an Exercise in 3D Analytic Geometry

针对一道空间解析几何习题,即求过给定点、平行于给定平面、且与给定直线相交的直线的方程,分别利用直线的点向式方程、平面的参数式方程、点到平面的距离公式、平面的一般式方程、平面束方程、平面的三点式方程以及向量混合积的几何意义等给出八种求解方法,旨在培养学生的发散性思维能力.

In this paper,eight approaches are presented to solve the problem of seeking the equation of straight line which passes a given point,parallels to a given plane,and intersects a given straight line.The approaches include the use of the point-vector equation of the straight line,the parametric equation of the plane,the distance formula between the point and plane,the general equation of the plane,the pencil of planes equation,the three-point equation of the plane,and the geometric meaning of the mixed product of vectors,etc.We aim on the students' divergent thinking ability.