名校
1 . 如图,在三棱柱
中,M为
的中点,设
,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/f4da81bc-ed3a-4026-93fd-db130c0db4d8.png?resizew=134)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79f2cfa5e197f859d8cac3d2287ece9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e72403ac1926f555073d01fa22ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf9d421e75be0122791cd2cd4b1cfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347a2f174217898b8148515dc29ab948.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/f4da81bc-ed3a-4026-93fd-db130c0db4d8.png?resizew=134)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图,在四面体
中,
,
,
,
,
,
,M为
的重心,N为
的外心,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07dcf0b16163e0e0e0c0f248466ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356dec89411835536e230aa792bd0ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b529582d676cbe4c12bb806db6013f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183ec02812ee8cda06c714eb3cee0ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc52a06d806fde891e09a0a389fcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/3b81533d-a484-46e0-a82e-61c78d7771fc.png?resizew=150)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
3 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc898591206900808334db44311ec95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf32bf961e6c83464b298b1ba8dc705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6123f13e3efcf5a6bd142d9fbbe5f84d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 如图,在三棱柱
中,
,
,
,
是线段
上的点,且
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4ea5586a-0d41-4a61-9ec2-9c7bd545d56a.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6eb2c0c1b3f47e344a4d0c49286a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af2626608f61a4cfbb86494bd6df0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487179b3b9fe9fed6b432b44f560a29e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4ea5586a-0d41-4a61-9ec2-9c7bd545d56a.png?resizew=171)
A.![]() | B.![]() |
C.![]() | D.直线![]() ![]() ![]() |
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名校
解题方法
5 . 如图,在直三棱柱
中,
,
分别为
,
的中点.
,求
的值;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c45fb1bd3936fe41d53ea3ac772bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d86dcb456ab7ae39a37c70b372848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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名校
6 . 如图,在四面体
中,点E,F分别是
,
的中点,点G是线段
上靠近点E的一个三等分点,令
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381985fdee6a1ac3ad4a73f5f653b84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8230c008759598844822bf52562e08e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知三棱锥O—ABC,点M,N分别为线段AB,OC的中点,且
,
,
,用
,
,
表示
,则
等于( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/2f07f920-920d-49b2-bb42-97c0f41912f7.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07dcf0b16163e0e0e0c0f248466ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/2f07f920-920d-49b2-bb42-97c0f41912f7.png?resizew=164)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 如图,在三棱台
中,且
,设
,点
在棱
上,满足
,若
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/2df24d7c-ded1-4551-a465-b5d6ec62c68c.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a09fe477818584028f82a09f1d19a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4276d5218e243b87f24eb68705247b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3df7a876bbef92c8b8d6a0d90df3381.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/2df24d7c-ded1-4551-a465-b5d6ec62c68c.png?resizew=166)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 如图,在平行六面体
中,
与
的交点,记为
,设
,
,
,则下列向量中与
相等的向量是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/37762131-f71c-4f50-9d33-0ffd16e28d9d.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef36fa79d02dd76e9ac5fda1689268f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9206f052cc7298fdf9049f9386f53928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381985fdee6a1ac3ad4a73f5f653b84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea141f0d6a89e23b855b7fabbc4b4a99.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/37762131-f71c-4f50-9d33-0ffd16e28d9d.png?resizew=171)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
10 . 如图,在棱长为4的正四面体
中,
是
的中点,
,记
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/a7bd56e6-78be-42bd-8d4e-5f7d6a01d14f.png?resizew=187)
(1)求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057505ce7b11cfb85e490cc44e88ccc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e306327dbe115902d2fe451395b48b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/a7bd56e6-78be-42bd-8d4e-5f7d6a01d14f.png?resizew=187)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41d51041342c5ffbb4359a3ac33342d.png)
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