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正三棱柱ABC-A1B1C1的底面边长为2,侧棱长为,D为A1C1中点,则直线AA1与面A...
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正三棱柱ABC-A
1B
1C
1的底面边长为2,侧棱长为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAASCAYAAACEnoQPAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAC/SURBVDhPzZNBEsUQEETnXBaOY+8m1g5iOwfJ
wlH6ZwRJ8ItklVSpQmn9picIg4+IsDT+iUf77R59XMz2zEB7xIw7x44e2nI+zrASZl5PxZG5OskN
0WtQdp+Ku0ClhFXnVsyWUKp45nyrH3ggjvDaokQnRIRgchtMJZRfs8fV8KVHpVUhhDR1iqDcluat
WBKu3ZIDe2iyPi0SweF+FUtA/SM58G98ZscV9xH28A1cNzenQMq9E8tF4v7KuVCsin81ApctPDAe
KwAAAABJRU5ErkJggg==
)
,D为A
1C
1中点,则直线AA
1与面AB
1D所成角的正弦值为( )
A.
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jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAE+SURBVEhL1ZVBEoMwCEU5l4scx31u4joHcetB
XOQoNJCoQUmJHTvTOtNNhZfPJyCg8gAA9vwoFVoA7X819s8AMaBjfxyGmLV3exCDE4lb6X2Axadk
j4vWMdvEiMEBek+Q3F5fkWwFXLdPSTkrl3KosQEk3wUsniXEgr5SATiPRdq4V0My9+cCKCWVMmCe
Z46dBsBhWnNrakAp4SibAFobWUlWIQBJPJkIm3MnRcKDMZ1MKiSAkLnu3AXZTgFYpwFhmBSA1uzG
TSQVVwU3AFcP2skc+/61/Tap7ds+WtwzCmyR3/ZA5e+bp7qBDSFKF9Kt26dPTp7GuAJirEY3XWIv
F8gZ8v4e0ODU60eR0ATQydz7TwF8WDHTbTv8joItlnegWGmSYs+C4YMBkPuvr438ETkGzPDwgXH+
0WG6IesFHFzuvvNRQ5IAAAAASUVORK5CYII=
)
B.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAkCAYAAACAGLraAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEnSURBVEhL1VbLDcMgDPVcHBgndzbhzCBcGaQH
RnGBUOLwM0Sq1EaKFEX28/OL/Qhg5wIAXLljKowAeu+7sX8C4NSliXI30gsaOFQlKTwHgSkGD+A9
elLTqV0AkuyNRNhvISJ4NDLPxjOATMMblEEDaa6mAO2RFT4K2TiFo6tuA6y1KVYLQKFf6XkGgPGT
kjauUonJyWIMELWQSDq478IRqEcWFCBRLst1T26W6aUFgtDzFipxGrUii6kGHAAr4grAqhfkYmvu
03OoRsSdyp/Y8cgton0JIC9N6rvavppYh0FwHWmyibQOxAMwDsQD0Ihq83q6DkWM3vdQA1Kn40B7
LYTotM5F1LYJfg4YHRiA041no9AC0GOsOoW2vsLiKvT/D1aTf2Od30ezAB9bevfsAAAAAElFTkSu
QmCC
)
C.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAkCAYAAACAGLraAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEtSURBVEhL1ZW9FcMgDIQ1FwXjuGcT1wxC60Fc
eBQFIfyDEaDESRG/l8aWPu4k+wIoXACAmh+1Qgsg3Rdr/wywebRpPhb9xtrVM9i8LRp36zrA4mKz
w0Xa2HiIG3oL6BxBeL3uQhorSL5dbOIutnKqGQNIvvWYZxYRC7qLCsAwZWnT4YZkHlcFyJayDQgh
pNrZAJp55dVcAdnCaZsA0hqTElZRAKJ4GiLsk7spKmYwxZNJRQkgJPvmLZTrLADrbBDMLACkZTfe
RFJRK3gDUM+g3Zxq+4/HT6NaXfpIdd9RMBb56xl0+UIC3eubW2glkA7QSSAFoJ9AY0A+vUyg8/Md
ApL3TgJ9AGBLdv8juBHqLVQDLCNsqCDmbjeBFIB+AikB+i/keR7oz5IrHyt4AfeD2gbxv4OFAAAA
AElFTkSuQmCC
)
D.
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正三棱柱ABC-A1B1C1的底面边长为2,侧棱长为
,D为A1C1中点,则直线AA1与面AB1D所成角的正弦值为( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAkCAYAAACAGLraAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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D.
-
正三棱柱ABC-A1B1C1的底面边长为2,侧棱长为
,D为A1C1中点,则直线AA1与面AB1D所成角的正弦值为( )
A.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAkCAYAAACAGLraAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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D.
-
如图,正三棱柱ABC-A1B1C1中,底面边长为2,侧棱长为
,D为A1C1中点.
(Ⅰ)求证;BC1∥平面AB1D;
(Ⅱ)三棱锥B-AB1D的体积.
-
如图所示,在正三棱柱ABC-A1B1C1中,底面边长为a,侧棱长为
,D是棱A1C1的中点.
(Ⅰ)求证:BC1∥平面AB1D;
(Ⅱ)求二面角A1-AB1-D的大小.
-
如图所示,在正三棱柱ABC-A1B1C1中,底面边长为a,侧棱长为
,D是棱A1C1的中点.
(Ⅰ)求证:BC1∥平面AB1D;
(Ⅱ)求二面角A1-AB1-D的大小.
-
如图所示,在正三棱柱ABC-A1B1C1中,底面边长为a,侧棱长为
,D是棱A1C1的中点.
(Ⅰ)求证:BC1∥平面AB1D;
(Ⅱ)求二面角A1-AB1-D的大小;
(Ⅲ)求点C1到平面AB1D的距离.
-
如图所示,在正三棱柱ABC-A1B1C1中,底面边长为a,侧棱长为
,D是棱A1C1的中点.
(Ⅰ)求证:BC1∥平面AB1D;
(Ⅱ)求二面角A1-AB1-D的大小;
(Ⅲ)求点C1到平面AB1D的距离.
-
如图所示,在正三棱柱ABC-A1B1C1中,底面边长为a,侧棱长为
,D是棱A1C1的中点.
(Ⅰ)求证:BC1∥平面AB1D;
(Ⅱ)求二面角A1-AB1-D的大小;
(Ⅲ)求点C1到平面AB1D的距离.
-
如图,正三棱柱ABC-A1B1C1的底面边长为a,侧棱长为
,点D在棱A1C1上.
(1)若A1D=DC1,求证:直线BC1∥平面AB1D;
(2)若
,二面角A1-AB1-D平面角的大小为θ,求tanθ的值.
-
已知正三棱柱ABC-A1B1C1,若过面对角线AB1与另一面对角线BC1平行的平面交上底面A1B1C1的一边A1C1于点D.
(1)确定D的位置,并证明你的结论;
(2)证明:平面AB1D⊥平面AA1D.