Question

棱长为2的正方体ABCD-A1B1C1D1中,A1C1∩B1D1=O.OA与BD1所成角的余弦值

Answer 1

用向量吧,好算

以A为原点,分别以AB,AD,AA1为x,y,z轴建立坐标系O-xyz

则A(0,0,0),B(2,0,0),D1(0,2,2),O(1,1,2)

∴向量AO=(1,1,2),向量BD1=(-2,2,2)

∴cos

=向量AO●向量BD1/(|AO||BD!|)

=(-2+2+4)/(√6*3√2)=2√3/9

设OA与BD1所成角为锐角,余弦值为2√3/9