名校
1 . 如图:三棱柱
中,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399611519729664/3399741726941184/STEM/4b0e1135c33b48b6b61fe94845d2d00d.png?resizew=128)
(1)求
的长;
(2)若点
是棱
所在直线上的点,设
,当
时,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae085a6e115d9519419db9f3ee18ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598031e9c32cc829c5181e685cf8bb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2023/12/29/3399611519729664/3399741726941184/STEM/4b0e1135c33b48b6b61fe94845d2d00d.png?resizew=128)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a604466a9c8d10d557b3dfc43b547065.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ba627416dad7af38eec520e2fcd70e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793bb46a1588d171bd14e5dccd729aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-12-29更新
|
266次组卷
|
4卷引用:6.2 空间向量的坐标表示(3)
(已下线)6.2 空间向量的坐标表示(3)四川省成都市第十二中学2023-2024学年高二上学期第三学月月考(12月)数学试题江西省上饶市北大邦实验学校2023-2024学年高二上学期期末质量检测数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点5 空间向量基底法综合训练【基础版】
名校
2 . 如图,在平行六面体
中,底面
是边长为
的正方形,
,
,
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/bccf7b94-b556-46b0-9924-bd101e1bbffb.png?resizew=175)
(1)用空间的一组基
表示
,
;
(2)求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecbca919bff5a39a99dd7f867dd61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962ddfa6a45e5588279c2a93f142924a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/bccf7b94-b556-46b0-9924-bd101e1bbffb.png?resizew=175)
(1)用空间的一组基
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61202553a50520bd294788335789ac3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38dfb3f3d83fa111eb89009789e88b1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec970106aaa464503c646b309167b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31bfc148417ee8cc4dacf5a29098acd.png)
您最近一年使用:0次
3 . 已知
,
,
.
(1)求
的值;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447c49a84c33ab016d4666a301608528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df1d886444a67202243459763ee10ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24ddf581f0b540d0d68e171cfab0c4f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c933a0fde595abd7cfa8258d52cdc63b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3286f62051c0c144863158a1a32fe2b7.png)
您最近一年使用:0次
2023-12-23更新
|
532次组卷
|
3卷引用:6.2 空间向量的坐标表示(3)
名校
4 . 已知空间向量
.
(1)求
;
(2)判断
与
以及
与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9be0ea19a65bf3f4e2a45cb84575a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884e8f2d5835771fd49093a6709be3a0.png)
(2)判断
![](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/7b76118bdca6c463cfb19b66f30281c4.png)
您最近一年使用:0次
5 . 如图,在平行六面体
中,底面
是边长为1的正方形,侧棱
的长为2,且
. 求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/e2df731f-087c-4cf9-a4bf-e36c1433560f.png?resizew=173)
(1)
的长;
(2)直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6357a7626fd369d5f60eb16f711a6d09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/e2df731f-087c-4cf9-a4bf-e36c1433560f.png?resizew=173)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
6 . 如图,在三棱柱
中,侧面
与侧面
都是菱形,
,
.记
.
(1)用
表示
,并证明
;
(2)若
为棱
的中点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab724e71a5c81257dbcc970ae4e087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcc3114ae5565f7414363d3626649bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7b92264c6a0e4be7dc1e494c6f1dc3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/c7945335-de3f-4676-b2a5-8f54e115e324.png?resizew=160)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb0dbfda18f5cf552c4b38a2527a20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faac7a82235d53bb4b6abe7ee54951.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
7 . 如图,在棱长为4的正方体
中,
,设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/1313eeea-6d8e-4228-874a-1f50c4b67758.png?resizew=164)
(1)试用
,
,
表示
;
(2)求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25068e088bc3fc13c676fba0745825b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703ae3e64cc6dd0dc76af04d09752ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746e93697953271f729503a31727c4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d66421989fc8910c14c7e9a9af0cf0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/1313eeea-6d8e-4228-874a-1f50c4b67758.png?resizew=164)
(1)试用
![](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/ae54940f33b8714da5fe3b7546f8b3dc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
8 . 已知
,
,求
(1)
;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a122bd8522edd25181766122b0ba557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057f57c7f0234c700205f04e094387e4.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c5faf8fe34d25fd89a828bb4d43172.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b8e1c412968c6aceb3a77e67864924.png)
您最近一年使用:0次
解题方法
9 . 如图,四面体OABC各棱的棱长都是1,
是
的中点,
是
的中点,记
.
(1)用向量
表示向量
;
(2)利用向量法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352afb2166bc2d282d55bd7bba4388e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/69f241eb-bce4-4006-b7c2-d6b3c14f35f7.png?resizew=165)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fddc1f1c50aab4de7fff286d691b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21909dd065ccc349a2cbfd4c3cf4976b.png)
(2)利用向量法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e3fa2e4de57a4c067e79be7d798e7.png)
您最近一年使用:0次
2023-11-23更新
|
207次组卷
|
3卷引用:6.1 空间向量及其运算(4)
10 . 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)
您最近一年使用:0次
2023-11-15更新
|
389次组卷
|
5卷引用:6.1 空间向量及其运算(5)
(已下线)6.1 空间向量及其运算(5)贵州省2023-2024学年高二上学期11月期中联考数学试题辽宁省抚顺市六校2023-2024学年高二上学期期中考试数学试题陕西省汉中市多校联考2023-2024学年高二上学期12月月考数学试题(已下线)专题01 空间向量及其应用常考题型归纳(1)