用向量方法证明空间四边形对角线相互垂直的充要条件是对边平方和相等

为方便,下面#后的代表向量.#CD=#BD-#BC,#AC=#BC-#BA,#AD=#BD-#BA.对角线的点积:#AC·#BD=(#BC-#BA)·#BD=#BC·#BD-#BA·#BD 两组对边平方和分别为:AB2+CD2=AB2+(#BD-#BC)2=AB2+BD2+BC2-2#BD·#BC AD2+BC2=(#BD-#BA)2...