23-24高二上·上海·课后作业
1 . 已知
是平行六面体.设
是底面
的中心,
是侧面
的对角线
上的点,且
,设
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668b7f96888281bb83fe5c96411fc0cf.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545decfe4dd2dcf6f24da7363c1bd023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5757e6c28bc7651d76952457ad889a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ea23c136291a944c73c576a558203a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668b7f96888281bb83fe5c96411fc0cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/f5a26915-7b4a-46da-bba7-3bb81ea59e04.png?resizew=178)
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2 . 如图,在四面体
中,
分别是
上的点,且
是
和
的交点,以
为基底表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a337a934b801730321f67b0e5a0b144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85a08b7404da7ee0fa373540966176b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1408c55c40465b26758562f59d99ae41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/fb89f17c-87a6-403f-bc75-f41656266583.png?resizew=154)
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3 . 在三棱锥
中,
,
,点
在
上,
,
为
中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb53a5e73f95e3f46a34965c5c0ac73.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ccad4025134a601044fbc58f1cf4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3744bb598bb9292a98812dddf9fdb3cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6aa2a7c840613899fac45f7dd04789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb53a5e73f95e3f46a34965c5c0ac73.png)
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4 . 已知空间向量
的模长分别为1,2,3,且两两夹角均为
,点
为
的重心,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ad85b1b027a45ce5cbde9ed1fd9632.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12e912c56b58fc780489fab055aa94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ad85b1b027a45ce5cbde9ed1fd9632.png)
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2024高二上·全国·专题练习
5 . 在直三棱柱
中,
,
,D为
的中点,在如图所示的空间直角坐标系中,
的坐标分别为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead1d5ab63a76fc1fa2b0fef17c5c009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1f47b28ba9aeaae062a569871be770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be8094e10da5b004100472adca90bdd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/9792d481-d462-48e7-a663-cb259a559751.png?resizew=136)
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6 . 如图所示,在平行六面体
中,
,
,
,点M是
的中点,点
是
上的点,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e983af1dfd0891d331a18e80f829c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13447f65fda380f81d32ac3d7835a887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/0d281199-39b0-4bed-a3eb-c1deb06b8e85.png?resizew=165)
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名校
解题方法
7 . 如图,在三棱锥
中,
,点
在线段
上,且
,则直线
与直线
所成角的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c65156d88c8787bf697d6c4fd8f21e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0cf3de61b5492989ae2002e19de770a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2023/12/23/3395591015309312/3396069057093632/STEM/bf147f21eb464843ab74887eb976a6df.png?resizew=177)
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2023-12-24更新
|
830次组卷
|
4卷引用:专题02 求空间角及空间向量的应用(三大类型)
名校
8 . 在三棱锥
中,
在线段
上,满足
是平面
内任意一点,
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656a93925561a68ac02e7352c933085c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f98d6d60d31af127291c3d22a7aa5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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2023-11-25更新
|
540次组卷
|
5卷引用:专题01 空间向量与立体几何(1)
(已下线)专题01 空间向量与立体几何(1)(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)四川省成都市树德中学2023-2024学年高二上学期期中考试数学试题四川省内江市第二中学2023-2024学年高二上学期12月月考数学试题山东省枣庄市滕州市2023-2024学年高二上学期期末数学试题
9 . 在四面体ABCD中,点E满足
,F为BE的中点,且
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9621311d2323bbf59eaff8ae11c289e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f229b7f456182f141b7ae8c08f0737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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10 . 如图,在平行六面体
中,
, ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
则
=____ ,
=____ (
,
精确到0.1).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecd2fb9d59e0d9a46ea3062f566ff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369056cce7ae550158fa9c1c7772da59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc42fb48159c7259b66a719faa60459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721554f715d299b5e1974e58aae90897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df276e9b9424486d59c747f1227b213c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/c723fe5c-1995-442e-a813-ac30bfc335c9.png?resizew=156)
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