向量式参数方程所表直线位置关系的判定

Determination on the Spatial Relation of Straight Lines Presented by the Vector-type Parametric Equations

在运用高等代数中线性相关、线性无关、线性空间、以及生成子空间的相关理论的基础上,给出了用向量式参数方程所表示的空间直线共面和异面的两个判定定理,并且给出了三个推论用于在共面的情况下判断平行、相交、重合的情况.最后通过一个实例,说明了定理的应用.

Based on the theorems on linear dependence, linear independence, linear space and relevent theories concerning generation of sub-space in advance algebra, two theorems are given to determine whether the spatial straight lines, presented by the vector-type parametric equations are coplanar or not. Further, three corollaries are introduced to determine whether coplanar straight lines are parallel, intersectant or overlapping with each other. Lastly, an example is presented to demonstrate the appli- cation of the theorems.