1 . 平面两点
,
的坐标分别满足
和
.
为坐标原点,已知
,
且
,
.若存在
,使得
,则正实数
的值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe91700574eeb6d476da2ee518aaf8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f7c86a88e29273ba51dc9cb9bd1fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af6ac57bed38abc6580e77cc23d474b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c32f820ab76920e200b6018c9e3f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f995ae49f0bacd78664f5d11ccd42b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df2ee0ecb7d77899d352681febd9c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249dc5045b2d6d1fc384e80293285df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2 . 如图,棱长为2的正方体
的侧面
(含边界)内有一动点P,则下列结论中正确的是__________ .
①若
,则
;
②若
,则
;
③若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1fcf28d4dc52bd8eadeb29a4a26adf5.png)
④若
,则存在非零向量
使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/a33d42a6-5169-4aaf-b1fa-9c02f5e85b42.png?resizew=148)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ea08f801858780157d90ebfc2f9a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f08d1ad0c831f893b2f4c6c3ec5ac3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22816abb5db98d064692b1b1ea59363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715d94cc0da54657bf1bb8b48869502.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e414f02107ff50576e2a2c7a6ea93ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1fcf28d4dc52bd8eadeb29a4a26adf5.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f14e76a43852aa165a3e4702bf005f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5a2b21c3c5ef3fa229febbff103665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c6b1a61d9bab08721ec4f588084071.png)
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名校
解题方法
3 . 如图,已知四边形
是矩形,
平面
且
,
的中点
,则异面直线
与
所成角的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04c896027b8f76412762a7a16f3acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0f73b3c63084d9c032802e01f9a168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/a6cee657-9a60-49e4-8d29-aa7ac610aa6c.png?resizew=147)
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名校
4 . 已知命题“方程
至少有一个负实根”,若
为真命题的一个必要不充分条件为
,则实数
的取值范围是
您最近一年使用:0次
2023-11-10更新
|
763次组卷
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5卷引用:福建省福州市八县(市、区)一中2023-2024学年高一上学期11月期中联考数学试题
福建省福州市八县(市、区)一中2023-2024学年高一上学期11月期中联考数学试题江西省上饶市第二中学2023-2024学年高一上学期期中数学试题(已下线)高一上学期期末考试填空题压轴题50题专练-举一反三系列(已下线)专题01 集合与常用逻辑用语4-寒假作业单元合订本(已下线)第2题 条件探求与判断,转化构造直接法
5 . 已知单位向量
满足
,若
与
的夹角为
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bf31d9d07e454de95bf2878ede921a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcf00f0d422c0a8ea5b6de2dc42a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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名校
解题方法
6 . 在正四棱锥
中,若
,
,平面AEF与棱PD交于点G,则四棱锥
与四棱锥
的体积比为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120f8941f03c070168666baa80ef8c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70b3a2b50632e4441045cd65b94ffd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042dd94d956b294c889202cc9d0721db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2023高二·全国·专题练习
名校
7 . 如图,在平行六面体
中,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7046ea5ec8bb0f777482b086d181e2e9.png)
.则
与
所成角的余弦值为____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd21a4e45dc1beb069d7e78f84a51544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7046ea5ec8bb0f777482b086d181e2e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432aca761e9fa97d3728a8038de81e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a037b1a3ec2e37bbcb05d0a467efb511.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/8dbf7b4d-980d-49fb-963e-9e18ce41fa24.png?resizew=174)
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2023-10-20更新
|
531次组卷
|
4卷引用:1.2 空间向量基本定理【第二练】
(已下线)1.2 空间向量基本定理【第二练】广东省茂名市信宜市第二中学2023-2024学年高二上学期11月月考数学试题四川省成都市石室中学2023-2024学年高二上学期期末综合复习数学试题(一)(已下线)专题11 空间向量及其运算10种常见考法归类(3)
8 . 已知
,
,若
与
的夹角为钝角,则实数t的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52163a3b994fe69ff0fee8cb88a24462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d421b6979b436c4129d9ab2af3ba71b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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9 . 平行六面体
中,
,
,
,动点P在直线
上运动,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29325f51647dde45ffa565600d353d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b60e79fa5148edfa2409467fbafd42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/836b52ab-30f7-45d4-a755-2f7d434fee7e.png?resizew=178)
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2023-10-17更新
|
787次组卷
|
9卷引用:安徽省六安第一中学2022-2023学年高一下学期期末考试数学试卷
安徽省六安第一中学2022-2023学年高一下学期期末考试数学试卷北京市朝阳区北京工业大学附属中学2023-2024学年高二上学期10月月考数学试题(已下线)专题 01 空间基底及综合应用(2)(已下线)模块一 专题1 空间向量的基本运算 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)专题 01 空间基底及综合应用(1)(已下线)模块一 专题1 空间向量的基本运算 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)专题01 空间向量的线性运算(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)(已下线)期末精确押题之填空题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)第01讲 空间向量及其运算