如图在空间四边形abcd中ab垂直于cd,ac垂直于bd,求证ad垂直于bc.用向量法求
问题描述:
如图在空间四边形abcd中ab垂直于cd,ac垂直于bd,求证ad垂直于bc.用向量法求
答
AD*BC=(AC+CD)*(BA+AC)
=AC*BA+AC*AC+CD*BA+CD*AC
=AC*BA+AC*AC+CD*AC
=AC*(BA+AC+CD)
=AC*BD
=0
所以AD⊥BC