23-24高二上·上海·课后作业
1 . 根据下列方程,判定直线
与
的位置关系,若相交,求出夹角.
(1)
,
;
(2)
,
;
(3)
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15d419ac2b9832ef6fb704d98790487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db191a381bcc131aad1216844cfe0fc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00b8eb5fee88a104b321d1c2d5c5b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0031a6f0727e81ec9966c95fb2a5eb12.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83342b9d257e062198077c2897e77dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5810390abd0a156828293ad5885442d8.png)
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2 . 已知直线倾斜角
的范围是
,当
时,
等于直线的斜率值.则直线
的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f897eed68eaf69608ffa4cf9de94a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb9fe45c7d4dd213d9c640150daec06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfc6b5b7ae63a330f0cd8593ee47338.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 已知点P为椭圆
上除长轴端点外任意一点,
、
分别为椭圆的左焦点与右焦点,求
的最大值,并求此时点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
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4 . 已知等腰
的顶点为
,
,底边
所在直线的方程是
,分别求两腰所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fadc9a19de13ca7688ca93f0c70a8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d65edc05562c2e22e85d450cdb41e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86b8513235bf21981e84618d8849b00.png)
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2022-09-07更新
|
79次组卷
|
2卷引用:沪教版(2020) 选修第一册 同步跟踪练习 第1章 1.3~1.4阶段综合训练
5 . 求经过下列两点的直线的斜率和倾斜角.
(1)
、
;
(2)
、
,其中实数a是常数.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd2a841c0085d1ee70e13dadc4eade9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f20d28d9fd9dd2385f8665fa3fae80.png)
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6 . 双曲线
上的一点P与左右焦点
、
构成
.
(1)求
的内切圆与x轴正半轴相切的切点N的坐标;
(2)已知
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec547b073f963a99feadb396f8ed0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db8549b6869b86256580d48ba1a2c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
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解题方法
7 . 在正三棱柱
中,已知
,D在棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/2f92e9f7-3f3c-4ef9-a912-1d673c012b41.png?resizew=153)
(1)求二面角
的大小(用反三角函数值表示);
(2)求直线AD与平面
所成角的大小(用反三角函数值表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/2f92e9f7-3f3c-4ef9-a912-1d673c012b41.png?resizew=153)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
(2)求直线AD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
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解题方法
8 . 如图,在长方体
中,
,
,则
与平面
所成角的大小为______ ,
与平面
所成角的大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0af405392c66b86550a58f1cb9868717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8c1cf368-14e5-4924-85e5-62dfbce135b4.png?resizew=149)
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解题方法
9 . 如图,在直四棱柱
中,上底面ABCD为菱形且∠BAD=60°,侧面为正方形,E、F分别为
、
的中点,M是AC与BD的交点,则EF与
所成角的大小为___________ (用反三角函数表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e884ca9429486026caa5e2310b0e4e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962142434410496/2962989983391744/STEM/5db325dd-8da7-4db4-8e37-f432bedeebca.png?resizew=199)
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解题方法
10 . 如图,四棱锥
中,
平面ABCD,
,
,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d19abff9-1088-4a12-94a0-9ba582afc173.png?resizew=162)
(1)求三棱锥
的体积;
(2)求异面直线PC与AB所成角的大小(结果用反三角函数值表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e21b9210b503c2dc8efb9444375f45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d19abff9-1088-4a12-94a0-9ba582afc173.png?resizew=162)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482ee1668a59ca21f3ae8b6bad58eae.png)
(2)求异面直线PC与AB所成角的大小(结果用反三角函数值表示).
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