名校
解题方法
1 . 如图,在棱长均为1的正三棱柱
中,点
在棱
上,且
.记
,
,
.
表示
、
;
(2)求直线
与直线
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47ed867750dba3df7a4834827f272c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef36fa79d02dd76e9ac5fda1689268f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f8173bb7787b6b107acfe767dd1d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df107a0db8e7084e46cbf0edc9dd4878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2 . 如图,长方体
中,点E,F分别是
和BD的中点,
,
,
,将下列两组中相等的向量连线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08b344a0ebe520f4147702257aa276b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9a915b6183ce6418229dad5fec617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f639828509b293069c2782d049d22f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19537b6aa2888860ce6a8033d4a63fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a0e783537963d7ebd93b2e481c548e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8d06249c2993354ec165218a038265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea16abad79703e194ef022e430682021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08b344a0ebe520f4147702257aa276b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532a41ad7600bcb9eecb949fec58acee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb169a920a8286d127ba71b99f5c139b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9a915b6183ce6418229dad5fec617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9492b5602eba95ed7757f60687aaa1da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
您最近一年使用:0次
名校
3 . 在正方体
中,设
,
,
,
,
分别是
,
的中点.
(1)用向量
,
,
表示
,
;
(2)若
,求实数
,
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184359fe3cadc363cf4ebe586c2b3db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb353b74a350c3adfc1c6cd4e508849d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fe121e62557dbeeb40885d5aaeb801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6186e940de954238085c0c68ef9fcdf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
您最近一年使用:0次
名校
解题方法
4 . 如图所示,平行六面体
中,
.
表示向量
,并求
;
(2)求直线
与直线
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083e5ad385e6a0801801073f1cafadb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68873c59a21b0cd408cdf2b47d51096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccec46f7c4da972fef6e940158628242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33e3af60b6aa94f39bbd04470d2e404.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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5 . 在长方体
中,
,
,
,以
为原点,
、
、
所在直线分别为
轴、
轴、
轴的正方向,建立空间直角坐标系,则点
可用有序数组
表示.空间中任意一点可用有序数组
表示,定义空间中两点
,
的距离
.
为边
(含端点)上的动点,证明:
为定值;
(2)
,
,
为空间中任意三点,证明:
;
(3)若
,
,其中
、
、
,求满足
的点
的个数
,并证明从这
个点中任取11个点,其中必存在4个点,它们共面或者以它们为顶点的三棱锥体积不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5d5dc7fd9e2a9ebac16a4147979d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9ce42d7ae1d4b67045e78c3ab05f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9e23910557d245d6e7d5959d91e135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a334cd1d83ebe328877006f689e28bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c66066f64a28eb515f8de3a4e063292e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5ff1d52b11822af84e82488a9e546e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d594e1827f2d6d03295009b1ed75b3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f92b567c6128f0ada19a3b7a243abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb0dd80eb2f71473e399c1332ce71f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f0eabf0b9199ff58f94b72507b051a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50c35157956d1d4679598ee26bd408d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63a978622110d66c5fdb4c9ed08539b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c289e83620c6a6f873d116eed1e053f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba96eac12eb5f43f43b74d7f513f725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314bd1d7a6e070f4f2428f9a321804e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ecc49abb6be7701f68cfc09598c324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c7f3377167e892a662c15787b372f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
您最近一年使用:0次
名校
6 . 如图,三棱锥的棱长都相等,记
,
,
,点
在棱
上,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/fa8c53645db602c72b00b599c2c0ff97.png)
(2)若D是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bd1953f49c988de31592b844f79b83.png)
您最近一年使用:0次
名校
7 . 如图,在平行六面体
中,设
,
,
,
,
,
分别是棱
,
,
的中点,试用
,
,
表示以下各向量:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cc37b6cfb037ac5e114daeb3a3b68f.png)
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2cffd3340a20e1a05d6dfe215f3607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f8173bb7787b6b107acfe767dd1d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232311b4261c36b659555a07bfa00f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cc37b6cfb037ac5e114daeb3a3b68f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9048009c730b179d7cb1e7f2364c86be.png)
您最近一年使用:0次
解题方法
8 . 如图,在底面
为菱形的平行六面体
中,
分别在棱
上,且
,且
.
(1)求证:
共面;
(2)当
为何值时,
;
(3)若
,且
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5cdcc0d2cbcf7ebf6975618f3114d51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9196864f83e290af5ba64c4eb2c7ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/ef05bb8c-102a-4217-a2e1-1184e895085c.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b488a540540a2d6a4e3b8b5f67b04611.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6df10d0b03d6f6e640d9c5f3695a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1515a445310d259a080d02e16c2e58e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e44cb429eea46e7ee4320147192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccffde150c595f4e4d444f251c87b1d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
您最近一年使用:0次
2024-04-07更新
|
328次组卷
|
2卷引用:江苏省常州市联盟学校2023-2024学年高二下学期3月阶段调研数学试题
2024高三·全国·专题练习
9 . 如图,在平行六面体ABCD-A1B1C1D1中,设AA1=a,=b,
=c,M,N,P分别是AA1,BC,C1D1的中点.试用a,b,c表示以下各向量:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)A1N;
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76782c6299c144c919de3213c60a7e5f.png)
您最近一年使用:0次
2024高三·全国·专题练习
10 . 如图平行六面体
中,三棱
间夹角均为
.求:
(1)对角线
的长度;
(2)平行六面体全面积
;
(3)平行六面体体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92178a5c6a76586292f622da298a8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a12ffb2088a13eda785cb147122375e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/5a0bdf7f-a881-4e5c-8746-4fecfe952220.png?resizew=175)
(1)对角线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)平行六面体全面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e5c11ced8d1483c518ccd650924e47.png)
(3)平行六面体体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次