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证明直线与直线、直线与平面、平面与平面之间的平行与垂直问题,是立体几何中最常见也是最重要的问题.这类问题的求解,通常运用“降维”的思想,即将面面问题“降维”为线面问题,将线面问题“降维”为线线问题来处理,这是一种“化归”的思想.但如果借助平面法向量这个工具,也可以很简捷地解决问题.本文结合具体案例介绍用平面法向量来证明平行与垂直的问题.
It is the most common and important problem in solid geometry to prove the parallel and perpendicular problems between straight line and straight line, straight line and plane, plane and plane. The solution of such problems usually uses the idea of “dimension reduction” Face problem “dimension reduction ” for the line surface problem, the line surface problem “dimension reduction ” for the line problem to deal with, this is a kind of This tool can also be very simple to solve the problem.This paper combines the specific cases to prove the parallel and vertical problems with plane normal vector.