如图,在五面体
中,
平面
,
,
,M为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3ad0bd3a-3248-4ad2-835c-d6aca872922c.png?resizew=183)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147e7c8ba0bbb540a712f6eb2ed6d22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9001a8577e62e945edede16ff505f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4971053cca6577773936c64add531503.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3ad0bd3a-3248-4ad2-835c-d6aca872922c.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8a20c1fc8a5620db5db3a74eb01201.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8a20c1fc8a5620db5db3a74eb01201.png)
更新时间:2022-01-11 23:05:54
|
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【推荐1】已知四棱锥
中,底面ABCD是正方形,
平面ABCD,
,E是PB的中点.
(1)求直线BD与直线PC所成角的余弦值;
(2)求证:
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(3)求点
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(1)求直线BD与直线PC所成角的余弦值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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【推荐2】如图,在正三棱柱
中,所有棱长均为2,设
交于点
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2018/1/24/1867435599953920/1868958287208448/STEM/9d5d4e97adcb42deade23e3eac0f272f.png?resizew=126)
(1)证明:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1aef95c1700c7e7ce1dfaca755481e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2018/1/24/1867435599953920/1868958287208448/STEM/9d5d4e97adcb42deade23e3eac0f272f.png?resizew=126)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078a730c37b2d5118fde01c389f1c120.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44173facb75f58f9e8001ee198917851.png)
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解答题-问答题
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【推荐1】如图,在棱长为
的正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/a39f5529-3cce-43fa-9293-c25c6abd4cdf.png?resizew=184)
(1)求异面直线
与
所成的角的余弦值;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/a39f5529-3cce-43fa-9293-c25c6abd4cdf.png?resizew=184)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
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【推荐2】如图,在三棱柱
中,侧面
为正方形,平面
平面
,
,M,N分别为
,AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92aaa495-4659-4e6b-8b19-fb30bb71bfae.png?resizew=182)
(1)求证:
平面
;
(2)若
,求直线AB与平面BMN所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/92aaa495-4659-4e6b-8b19-fb30bb71bfae.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1be642ddd61c3ad26bcbe2dc42e3512.png)
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(0.85)
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【推荐3】如图,在四棱锥
中,底面
为正方形.且
平面
,M,N分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/4c443229-3af6-484b-ad11-f0c0729c306c.png?resizew=151)
(1)求证:
平面
;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930e85bc9f73e86cfb6ce9b076433f1b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/4c443229-3af6-484b-ad11-f0c0729c306c.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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