如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD=AA1=1 AB=2求平面A1BD与平面BCC1B1所成二面角的大小. (不能用向量方法作答)
如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD=AA1=1 AB=2求平面A1BD与平面BCC1B1所成二面角的大小. (不能用向量方法作答)
如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD
如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD=AA1=1 AB=2求平面A1BD与平面BCC1B1所成二面角的大小. (不能用向量方法作答)
如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD如图,ABCDA1B1C1D1是四棱柱,AA1⊥底面ABCD AB‖CD AB⊥AD,AD=CD=AA1=1 AB=2求平面A1BD与平面BCC1B1所成二面角的大小. (不能用向量方法作答)
作CE∥AD交AB于E,连AC,BD交于F,
ABCD-A1B1C1D1是四棱柱,AA1⊥底面ABCD,AB‖CD ,AB⊥AD,AD=CD=AA1=1 ,AB=2
易知AECD是正方形,F是△CDE的重心,DF=DB/3.
AC⊥BC,∴AC⊥平面BCC1B1.
A1C1∥AC,∴AC⊥平面BCC1B1.
∴△A1FB在平面BCC1B1的射影是△C1CB.
A1B=DB=√5,A1D=√2,取A1D的中点M,则BM⊥A1D,
BM=√(5-1/2)=3/√2,∴S△A1BD=(1/2)A1D*BM=3/2,
∴S△A1FB=(2/3)S△A1BD=1.
BC=√2,CC1=1,S△C1CB=1/√2,
设平面A1BD与平面BCC1B1所成二面角为θ,则
cosθ=S△C1CB/S△A1FB=1/√2,
∴θ=45°.