例析平面方程的几种解法

Illustration on ways of solving equation of a plane

平面方程可以分为的五种情形,即点法式、一般式、三点式、截距式和法线式,常用的是点法式、一般式.知道平面上的一个已知点和它的一个法向量,就可以确定这个平面.对平面的法向量,只要与这个平面垂直的任何非零向量都可作为该平面的法向量.法向量不惟一,但它们彼此平行.法向量常用向量的代数运算求得.找出法向量和找出平面上的点求出平面方程,是求平面方程的主要方法之一.着重研究用点法式和一般式求平面方程Ax+By+Cz+D=0,并探索在平面的一般方程中,待定系数A、B、C、D分别为零或不为零时的一些特殊平面方程及位置特征.

One of the ways to solve equation of a plane is to find normal vector and the point on the plane.By using related concepts of normal vector,algebraic operation and determinant calculation,one can solve equation of a plane.Equation of a plane can mainly be classified into the following five patterns,namely,pointnorm form,general form,three-point form,intercept form and normal form.This paper focuses on solving equations of pointnorm and general form,and pursues the placing feature of equation when the undetermined coefficient in equation of general norm is or is not zero.