高等数学研究
高等數學研究
고등수학연구
STUDIES IN COLLEGE MATHEMATICS
2014年
4期
77-79
,共3页
直线方程%平面方程%方向向量%法向量%距离
直線方程%平麵方程%方嚮嚮量%法嚮量%距離
직선방정%평면방정%방향향량%법향량%거리
equation of straight line%planar equation%direction vector%normal vector%distance
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。
針對一道空間解析幾何習題，即求過給定點、平行于給定平麵、且與給定直線相交的直線的方程，分彆利用直線的點嚮式方程、平麵的參數式方程、點到平麵的距離公式、平麵的一般式方程、平麵束方程、平麵的三點式方程以及嚮量混閤積的幾何意義等給齣八種求解方法，旨在培養學生的髮散性思維能力。
침대일도공간해석궤하습제，즉구과급정점、평행우급정평면、차여급정직선상교적직선적방정，분별이용직선적점향식방정、평면적삼수식방정、점도평면적거리공식、평면적일반식방정、평면속방정、평면적삼점식방정이급향량혼합적적궤하의의등급출팔충구해방법，지재배양학생적발산성사유능력。
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 .
