在棱长为1的正方体ABCD-A1B1C1D1中. (1)求:点A到平面BD1的距离; (2)求点A1到平面AB1D1的距离; (3)求平面AB1D1与平面BC1D的距离; (4)求直线AB到CDA1B1的距离.
在棱长为1的正方体ABCD-A1B1C1D1中.
(1)求:点A到平面BD1的距离;
(2)求点A1到平面AB1D1的距离;
(3)求平面AB1D1与平面BC1D的距离;
(4)求直线AB到CDA1B1的距离.
数学人气:835 ℃时间:2019-08-20 00:33:53
优质解答
(1)因为点A在平面BD
1内
∴点A到平面BD
1的距离为0
(2)正方体的体对角线为
而点A
1到平面AB
1D
1的距离是正方体的体对角线的
∴点A
1到平面AB
1D
1的距离为
;
(3)平面AB
1D
1∥平面BC
1D
这两个平面将体对角线分成三等分
∴平面AB
1D
1与平面BC
1D的距离为
;
(4)∵AO⊥A
1D
∴A到CDA
1B
1的距离为AO=
而AB∥平面CDA
1B
1∴直线AB到CDA
1B
1的距离
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