名校
1 . 空间四边形
中,设
,
,
,点
在棱
上,且
,
是棱
的中点,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/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/8926ddd0b69d714c7310cc5bf23d199d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 在三棱柱
中,D,E,F,G分别为棱
,
,
,
的中点,若
,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/76fb80aa-d0a2-4deb-83ef-9725993045cd.png?resizew=161)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb428e0cfc07acab10e19aff3fab8ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db57b8df3b11a1bcd1a6b9815ed7d674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7471558c3441108b958988557aeeb6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde7b80040918e501fe62e0b0048b749.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/76fb80aa-d0a2-4deb-83ef-9725993045cd.png?resizew=161)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 在三棱锥
中,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dfbc030288a6019524e31151ad89dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf69b83153f6ec578b83e09d688a877.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 如图,在三棱柱
中,
分别为
和
的中点,设
.
(1)用
表示向量
;
(2)若
,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb5f474b6067ce50ca48790c45fd587.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/e1aec47f-0dba-4964-a4ee-64f4bd3ec162.png?resizew=162)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9523d53df3a91e8bc9abaee19a1fb753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981978eee3927889e8527272c98468b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9eac7e04c7e650dfbf10ea05ea6045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5a8d419738d657c20fa8d1ba91c053.png)
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解题方法
5 . 如图,正方体
的棱长为
,
是
的中点,点
满足
,其中
,
,则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/c9c653a4-4190-4817-a378-c689e4127eb4.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3326f83861572391d3e78234573ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/c9c653a4-4190-4817-a378-c689e4127eb4.png?resizew=176)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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6 . 已知空间三点
、
、
,则以
、
为邻边的平行四边形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9c668b4f8cfaeab82fe4beb5ed1a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebdcfc1a82f1e38a1f9cecf7a969023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4886655e4272d2a5eb40adf508e4aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知点
为
所在平面内一点,
为平面
外一点,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63097cccecf24687f87c77057153f971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 在正方体
中,
是棱
上一点,
是棱
上一点,
,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/58b432067f8dd0cd2ba829a884dc5edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6214fb4c3a4d7d404ed99db1b27f6242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图,在四面体
中,
,
,
,点
在棱
上,点
在棱
上,且
,
,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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.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/9bbd730783a9824a58001f6ced741adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d5e22578854c3bbd960b39eb0c64e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/14/49a27a89-08be-4fdd-bc2a-bd7d73dc20b5.png?resizew=144)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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10 . 已知向量
,
,
,若向量
与向量
,
共面,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f822cbe2d0993fd04000d33c68b0a7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fede89ef73bbd9cfaf1e40137fc90209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced68a7f1379fde0eecc850f3797538c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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