也谈直线和平面投影阵的应用

Projection of a Vector to a Straight Line or a Plane and Its Applications

针对空间解析几何中的投影与垂直问题,引入直线和平面的投影阵与投影公式,从计算空间角与距离,体积和对称以及判断直线共面等方面给出求解结论,以展示投影阵在理论推导和实际计算中的应用.

Projection is a useful concept in analytic geometry. In this paper, we present the matrix forms of the projections of a vector to a straight line, as well as to a plane, and illustrate the use of these forms in calculating various quantities and geometric properties in analytic geometry, such as distance, dihedral angle, volume, symmetric points and a plane containing three lines.