2024高三·全国·专题练习
1 . 已知空间中三点A(2,0,-2),B(1,-1,-2),C(3,0,-4),设向量a=,b=
.
(1)若|c|=3,且c∥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
(2)已知向量ka+b与b互相垂直,求实数k的值;
(3)若点P(1,-1,m)在平面ABC内,求实数m的值.
您最近一年使用:0次
2 . 如图,在正四棱柱
中,
.点E,F,G,H分别在棱
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/cc3d4739-9c86-444f-bb35-a421b503434a.png?resizew=113)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed5e5d514bba98dbd038d0857a34ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bb3bb65447a6d1c8d2891d9c8f8bdf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/cc3d4739-9c86-444f-bb35-a421b503434a.png?resizew=113)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5c87a4eeba6042558a1a7cc31b5c1d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b6917095bea8efd3154b72d737f013.png)
您最近一年使用:0次
名校
3 . 在空间直角坐标系中,已知点
,
,
.
(1)若A,B,C三点共线,求a和b的值;
(2)已知
,
,且A,B,C,D四点共面,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3d1559b293defb28b4570580ca1f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f23ae5c8e69fe196f997ca7184ac66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5b6f5aaae52b812be8e8b4aae3197c.png)
(1)若A,B,C三点共线,求a和b的值;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce4430b8b9b0c78de693513a7f88915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d2a3ce46b5ad55352501120930b51e.png)
您最近一年使用:0次
2023-10-24更新
|
316次组卷
|
5卷引用:广东省佛山市南海区大沥高级中学2023-2024学年高二上学期阶段检测一数学试题
广东省佛山市南海区大沥高级中学2023-2024学年高二上学期阶段检测一数学试题广东省江门市新会第一中学2023-2024学年高二上学期期中考试数学试题(已下线)模块二 专题1 利用空间向量对共线和共面问题的探究与应用 期末终极研习高二人教A版广东省江门市某校2023-2024学年高二上学期期中考试数学试题(已下线)专题4 大题分类练(空间向量与立体几何)基础夯实练 高二期末
4 . 已知
,
,
,且
,
.求:
(1)
,
,
;
(2)
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6613e0da7934bf8516726eda58e3279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c041e0c98b2c95f54a824a26c3d81b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e4b199691f2e39679de34eb42d7c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d76ee2e81f447f84a3e0b39c0388ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f622a667018a0a1b7b9334909c136090.png)
(1)
![](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)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e3921e92ab4a807bfb6e793240d879.png)
您最近一年使用:0次
解题方法
5 . 已知空间直角坐标系中的三点
,
,
.
(1)若
,且
∥
,求向量
的坐标;
(2)已知向量
与
互相垂直,求k的值;
(3)求点B到直线AC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5e428213f946350934bc876fba5514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca2df16b221585c93109fd17bc1b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92ecb2412db3b9143c500555c2a0ceb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3361b587b611701daf8078c1b2d8e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215ec17116710e7927ad75ccd88c4e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
(3)求点B到直线AC的距离.
您最近一年使用:0次
名校
6 . 四棱柱
的六个面都是平行四边形,点
在对角线
上,且
,点
在对角线
上,且
.
(1)设向量
,
,
,用
、
、
表示向量
、
;
(2)若
、
、
三点共线,求实数
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724a298d2319f26dc085f09b5169125c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fd9a92fe86ce127b606f01333f8986.png)
(1)设向量
![](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/39b0ff98fe5e0a913ebecda552acc6f6.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/afdb48133ed00fa1327ac46ca7f344b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ef300fccd1d15cfd5556f9d742e12f.png)
(2)若
![](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/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
7 . 如图,平行六面体
中,点M在线段
上,且
,点N在线段
上,且
.求证:M,N,
三点在一条直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bfbf0f38638236ea1b1a96ed04dee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71594be1602bece8a76509363cdbdff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/b978ae31-3c45-4c68-98ee-63b91ba2b7cc.png?resizew=154)
您最近一年使用:0次
名校
8 . 如图,已知
分别为四面体
的面
与面
的重心,
为
上一点,且
.设
.
(1)请用
表示
;
(2)求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905943d59ef17fdb1d29b626b0847d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb0493ebe599f2bc513e63e908bfd45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/25/98a3a9cf-687c-4a6e-b67e-ee4f9fa8ba54.png?resizew=167)
(1)请用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed18a92338c7578c18a5ba3a2ae1ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350f162ee9aa08f4c9779481a5ef1025.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b772d03da5f597caaf8ab796e564b7d.png)
您最近一年使用:0次
9 . 已知
为坐标原点,在四面体
中,
,直线AD∥BC,并且
交坐标平面
于点
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034545ebbadb7c5aefdfe4324253b68c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
10 . 已知点
,
是直线l上的两点.
(1)求直线l的一个方向向量;
(2)判断点
是否在直线l上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cb141eaf6c8146304d0bf6dc9bd379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c63d58f2a8b881b1f5599a2aaedf445.png)
(1)求直线l的一个方向向量;
(2)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edefddd404606e9e8abbda760f6ddb3.png)
您最近一年使用:0次