如图,平行六面体
的棱长均相等,
,点
分别是棱
的中点.
(1)求证:
平面
;
(2)求直线
与底面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa55c6ef551cb92a87525e90b20b0575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7fcac9c20f6236a7aca7c79dfdea99.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/aca4b60f-4c02-41e8-b4cc-c78b449d19e2.png?resizew=197)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
21-22高一下·安徽滁州·期末 查看更多[3]
安徽省滁州市2021-2022学年高一下学期期末教学质量监测数学试题江西省吉安市吉州区部分学校联考2022-2023学年高一下学期7月期末联考数学试题(已下线)第08讲 拓展二:直线与平面所成角的传统法与向量法(含探索性问题)(6类热点题型讲练)
更新时间:2023-06-24 11:21:30
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相似题推荐
【推荐1】如图,在三棱柱
中,侧棱垂直于底面,
分别是
的中点.
(1)求证: 平面
平面
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(2)求证:
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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(1)求证: 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/7bc75e06-eaf5-400f-bd96-6146a5f0ee75.png?resizew=135)
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解答题-证明题
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(0.65)
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【推荐2】如图,在四棱锥
中,底面
是平行四边形,
分别为
的中点,
为线段
上一点,且
.
平面
;
(2)若四棱锥
为正四棱锥,且
,求四棱锥
的外接球与正四棱锥
的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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解题方法
【推荐3】如图,在正四棱柱ABCD-A1B1C1D1中,E为AD的中点,F为B1C1的中点.
(1)求证:A1F∥平面ECC1;
(2)在CD上是否存在一点G,使BG⊥平面ECC1?若存在,请确定点G的位置,并证明你的结论,若不存在,请说明理由.
(1)求证:A1F∥平面ECC1;
(2)在CD上是否存在一点G,使BG⊥平面ECC1?若存在,请确定点G的位置,并证明你的结论,若不存在,请说明理由.
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【推荐1】在四棱锥P–ABCD中,底面ABCD是边长为6的正方形,PD平面ABCD,PD=8.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/03245e16-dacc-4148-8b26-021e54e8d30e.png?resizew=150)
(1)求异面直线PB与DC所成角的正切值;
(2)求PA与平面PBD所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/03245e16-dacc-4148-8b26-021e54e8d30e.png?resizew=150)
(1)求异面直线PB与DC所成角的正切值;
(2)求PA与平面PBD所成角的正弦值.
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【推荐2】如图,在四棱锥
中,底面ABCD是边长为1正方形,
底面ABCD,
,点
,
分别为棱PD,BC的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/5/2834263856185344/2847775103016960/STEM/17948e2b-e291-4d93-903f-f601965028ab.png?resizew=250)
(1)求证:直线
平面PAB;
(2)设点E在棱PC上,若
,求直线MN和平面EBD所成角的正弦值.
![](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/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2834263856185344/2847775103016960/STEM/17948e2b-e291-4d93-903f-f601965028ab.png?resizew=250)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
(2)设点E在棱PC上,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b384315ba84cafb978ef3619c8162b5.png)
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【推荐3】如图所示,在正四棱锥
中,O为底面正方形的中心,E为侧棱PB上的动点.侧面PAD与底面ABCD所成的二面角的平面角为60°.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878631621091328/2892985233072128/STEM/ed5c4e00-a72d-472d-b4ff-2bbeafb5571b.png?resizew=180)
(1)求侧棱PA与底面ABCD所成的角的正切值;
(2)若
,问在棱AD上是否存在一点F,使
侧面PBC,若存在,试确定点F的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878631621091328/2892985233072128/STEM/ed5c4e00-a72d-472d-b4ff-2bbeafb5571b.png?resizew=180)
(1)求侧棱PA与底面ABCD所成的角的正切值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ada8c6bf90da64d90d00bc6c586af7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
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