Question

高中空间向量题求助

Answer 1

→AB•→CD
=(→AA'+→A'B'+→B'B)•→CD
=→AA'•→CD+→A'B'•→CD+→BB'•→CD
=0+→A'B'•(→CC'+→C'D'+→D'D)+0
=→A'B'•→CC'+→A'B'•→C'D'+→A'B'• D'D
=0+→A'B'•→C'D'+0
=→A'B'•→C'D'

Answer 2

过A作AE垂直AA'于E，过D作DF垂直CC'于F。

追答

AB·CD=(AE+EB)(CF+FD)=AE·CF+EB·CF+AE·FE+EB·FD=AE·FD=A'B'·C'D'