Question

在平行六面体ABCD-A'B'C'D'中,AB=4,AD=3,AA'=5,角BAD=90度,角BAA'=角DAA'=60

Answer 1

用向量法

向量AC'=AC+CC'=AB+BC+CC',

AC'^2=AB^2+BC^2+CC'^2+2AB·BC+2AB·CC’+2BC·CC’

=|AB|^2+|BC|^2+|CC'|^2+2|AB||BC*cos90°+2|AB||CC'|cos60°+2|BC||CC'|cos60°

=16+9+25+2*4*3*0+2*4*5*1/2+2*3*5*1/2

=85,

|AC'|=√85