组卷网>知识点选题>向量法求线线、线面、面面角
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解答题 | 一般(0.65) | 2021·山东高三其他模拟
1 . 在正六棱柱eqId4bc04427dad44ab68e6bc17043f2db69中,eqId48e2e8bb40184facbb0f028cc007b3ee.
说明: figure
(1)求eqId0627be51821d4be7b3e024a354815d64到平面eqId67375c9ffad947b4807f4c1535c51a9e的距离;
(2)求二面角eqId24441960ec894dcf98732aaced487289的余弦值.
解答题 | 一般(0.65) | 2021·浙江高二期末
2 . 如图,在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqId71244e6ba07c460fa53ad8370a5a0d0d底面eqId5ce7a06ae7a34393b92b5277978ac014,底面eqId5ce7a06ae7a34393b92b5277978ac014为梯形,eqIdeec1827a5d2841888521a9471977822deqIdf0ad309b98cf449cbb8337899f6fa4aa,且eqIda3e4dbffea7d4365bbc5ddbb8085b0a6
说明: figure
(1)若点FeqIdd293923b221045898dcc5442f88aa67a上一点且eqId70bfbc83f14c4730abda57b4c978cee8,证明:eqIde171c0f98d4c4668b6b2783bc491091e平面eqIdfcd3aba6b7804fb68706ce7697ffa7a3
(2)求直线eqIdd3a908032e2b40df95a6d86089b3f682与平面eqId8d5158cfa6f04afc87480399685f125f所成角的正弦值.
更新:2021/06/16组卷:0
3 . 如图,多面体ABCDEF中,底面ABCD为正方形,EAeqIdaac131017fe1430fb2c218bad7fdccd2FC,且EA=FC=AB=4,△EBD、△FBD都是正三角形.
说明: figure
(1)证明:CF⊥平面ABCD
(2)若eqIdbf4d6ee71f974ee8ba0d71bb42b71d59,求ME与平面BDF所成角的正弦值.
解答题 | 较易(0.85) | 2021·浙江高一期末
4 . 如图(1),在等腰梯形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId37d29a32dc044f1a8b15294574d026d9.将eqId16396ab536cf462399ed2cefb9763997沿直线eqId1b51efe7c2fa42748ac5a6be262e2fa4折起,使点eqId052844cae8574a8ab842c38a039baac0移动到点eqIdbedf755e0fdb4d078d6859360706b163(如图(2)),且eqIde098098b30814354a0ce4120350bfb9f
说明: figure
(1)求证:eqIdfa5db6312a9e4f5791b80e7607bc44de
(2)求直线eqIdd293923b221045898dcc5442f88aa67a与平面eqId0902deb68f0b430f932caadd41cd761a所成角的正弦值;
(3)求平面eqId0902deb68f0b430f932caadd41cd761a与平面eqId83e13ba429bb426fb39bd7720a82c64c的夹角的余弦值.
更新:2021/06/15组卷:0
5 . 在四棱锥P-ABCD中,侧面eqId3084aa1e379e4f168e9c2332df2ca9df底面ABCDeqId51f3ec023aab4a4ca875aaacec8ee06b为等边三角形,底面ABCD为菱形,eqId1d93035e412a49ceb13bf50eea803774OAD的中点.
说明: figure
(1)试在线段BP上找一点E,使eqId8beda2d2be2044da805962ee52e53b73平面PCD,并说明理由;
(2)求直线PC与平面PAB所成角的正弦值.
解答题 | 一般(0.65) | 2021·浙江高二期末
6 . 如图四棱锥eqIdac097205e9cb41279269aadcac3fb6f1的底面是正方形,eqId37ccc9c7e8054855b398776439996694,点eqId93cbffaa5ae045d6ac45d1e979991c3a在棱eqId0fd9ac73d66042c6bbd74f8ccdcbd9fc上,eqId2efda802d5534f6d92d9f8af7aaec28beqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4的交点.
说明: figure
(1)求证:平面eqId4fafeee649d04344b335a39b0b7d4843平面eqId91d4a39b7ad144abad9ea14eb250da8f
(2)当eqId93cbffaa5ae045d6ac45d1e979991c3aeqId0fd9ac73d66042c6bbd74f8ccdcbd9fc的中点时,求证:eqId48fbde4848cc4807a5c64f3d7a216e1b平面eqIdf98281520b2947568ec1ded4414173f4
(3)当eqIdaf93b124f0e04d5b8f32cab1f8b5c1ba是正三角形时,且eqId93cbffaa5ae045d6ac45d1e979991c3aeqId0fd9ac73d66042c6bbd74f8ccdcbd9fc的中点时,求eqId7111d4972b7c401c903ff4927c13b5ec与平面eqId0902deb68f0b430f932caadd41cd761a所成的角的正弦值.
更新:2021/06/14组卷:0
7 . 如图,已知多面体ABCD-eqIdae87f3c9c4af42d4b49b160bfeb53881AA1BB1CC1DD1均垂直于平面ABCDAD//BCAB=BC=CD=AA1=CC1=2,BB1=1,AD=DD1=4.
说明: figure
(1)证明∶eqId17ceafc9b1a74a37a89907801af1e742⊥平面eqId0645bf529ddb4f81b26e3a3c58a047b5
(2)求直线BC1与平面AB1C1所成的角的正弦值.
解答题 | 较易(0.85) | 2021·浙江高二期末
8 . 如图,在正三棱柱eqId227b4fe70ee049209073871a55fefc64与四棱锥eqId43fa6562e67b4f54862a7829a2ee7015组成的组合体中,底面eqId5ce7a06ae7a34393b92b5277978ac014恰好是边长为2菱形,且eqId4f9719429d8d4ea28525c6ebeed4a10d
说明: figure
(1)求证:eqIda687197ad6b048909a86cec9e9467f8f平面eqId50dcbbdb425943e8b5a0e6b8b508d09f
(2)设EeqId1b51efe7c2fa42748ac5a6be262e2fa4的中点,求直线eqId882aa90c519041b78217fa6e7b4d9a89与直线eqIdce3304c847ca47f486f045a4fbfc0ecd所成角的余弦值.
更新:2021/06/13组卷:0
填空题 | 一般(0.65) | 2021·浙江高二期末
9 . 如图在四棱锥eqId33081a2b430e4bd680b2820b7a880223中,eqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014eqId6bcdd2ee36c54403b8981b3d682dcf55eqIdca6267995e0548eea7942185d834ecfdeqIdfe18ffe719a14cd2a8848c7f519d9ecfeqIdb7f0098eb6da4659a0e864a5df45fb2beqIdbe1938fa020248698a5ed4e809883552E是直线eqId0fd9ac73d66042c6bbd74f8ccdcbd9fc上的一个动点,则eqId7111d4972b7c401c903ff4927c13b5ec与平面eqId0c401a91a4414c55b1765c810dd46b52所成角的最大值为________
说明: figure
更新:2021/06/13组卷:0
解答题 | 较易(0.85) | 2021·浙江高二期末
10 . 在等腰梯形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId6bcdd2ee36c54403b8981b3d682dcf55eqId4102d7501cb94241b9ff8bebff79a700eqIdbc275702ba1c4c31a739543df87a50b1EeqId34c6b6e427744abfb88dc90b8c7c2111中点,将eqId17f1a7d90f314522bf04ade3b7bd22ba沿着eqId1dcb20a9ce8d4076af5dd64f7066c6d6折起,点C变成点P,此时eqId29f3304d49ea487caa023e3fc568a084
说明: figure
(1)求证:eqId3f4d7c2ca35446ab97cc2f02e69cee94
(2)求直线eqIdd293923b221045898dcc5442f88aa67a与平面eqId0902deb68f0b430f932caadd41cd761a所成角的正弦值.
更新:2021/06/13组卷:0
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