如图,在三棱锥
中,平面
平面
,
,
,
分别为
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848859527716864/2849639249453056/STEM/bf47cd72-f084-48f7-a735-fe26c9b1dff8.png)
(1)求点
到直线
的距离
(2)求平面
与平面
夹角的余弦值
(3)已知
是平面
内一点,点
为
中点,且
平面
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ed20e68b1df31a3d7dfd31b427bef.png)
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848859527716864/2849639249453056/STEM/bf47cd72-f084-48f7-a735-fe26c9b1dff8.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
更新时间:2021-11-12 12:28:48
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图,在四棱锥
,底面
为梯形,且
,
,等边三角形
所在的平面垂直于底面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/c307960c-c77a-44ed-8f41-103bc2e0b9a8.png?resizew=220)
(1)求证:
平面
;
(2)若直线
与平面
所成角的正弦值为
,求二面角
的余弦值.
![](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/e306e30d3159e4a68435c3fcfc8da693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90197a948331e61db644266368017e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/c307960c-c77a-44ed-8f41-103bc2e0b9a8.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】在如图所示的圆台中,
是下底面圆
的直径,
是上底面圆
的直径,
是圆台的一条母线.
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/d8dfa2d9ecab4a0bac28eb4cb0ea2d11.png)
(1)已知
分别为
的中点,求证:
;
(2)已知
,
,求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/c2026a00dac745a68d4be98ea57eb968.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/a994fec3fcf7465893f75c85217ef6ed.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/0417464253404fc491a1b3f2c534446d.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/315207c4cfdc43f487d79597ecc3af03.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/59ae6b20c1c44748857ac45f52020115.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/d8dfa2d9ecab4a0bac28eb4cb0ea2d11.png)
(1)已知
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/9421fba81f044da9927d1133821ca8b1.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/33636cafc63c46508c6d51a7dd3e22d5.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/3b5afd95420043b48d0f0b9ce314d996.png)
(2)已知
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/1018033148a743d9a84f8b7d80c4a7fa.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/c6d9212110084093b3757a8bc01a3f03.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021933821952/1573021939400704/STEM/757b3eb9e96f4cf98b32ada934b17a44.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐1】如图1,梯形
中,
,过
,
分别作
,
,垂足分别为
、
.若
,
,
,将梯形
沿
,
折起,且平面
平面
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/44a7ff66-294e-43ea-bd1d-548ba66dcf2f.png?resizew=332)
(1)证明:
;
(2)若
,在线段
上是否存在一点
,使得直线
与平面
所成角的正弦值为
,若存在,求出
的长,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ff7bf8ffc8a04186e3e13c1a6d5ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe38a76667fa89be7cafe65266aa65a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/44a7ff66-294e-43ea-bd1d-548ba66dcf2f.png?resizew=332)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c7e72ef83184b96b12a51daf32c220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743c08870d66a766fa25298adf4dbf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】如图,在三棱锥
中,平面
平面
,
,
,D,E分别为
,
中点,且
.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986405733171200/2987120984604672/STEM/cf462bab8c594ce3af86fa2de2d7bad5.png?resizew=218)
(1)求
的值;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3735a467f788624fe63946e0da5b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986405733171200/2987120984604672/STEM/cf462bab8c594ce3af86fa2de2d7bad5.png?resizew=218)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2465ee1fec12351943f15055dfd6ec73.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d682fd0344452998187cb6d48de3dd1.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐3】如图,在四棱锥
中,四边形
为平行四边形,其中
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/156a71c3-35e1-4374-8c18-d4a2ffa7f4e8.png?resizew=181)
(1)证明:
平面
;
(2)若锐二面角
的余弦值为
,求该四棱锥的体积.
![](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/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900a8f4c8349e1c79e8dc31a493b5964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/31/156a71c3-35e1-4374-8c18-d4a2ffa7f4e8.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7d6e5be7914a224e94a7b7e409a79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
您最近一年使用:0次
解答题-证明题
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适中
(0.65)
名校
【推荐1】如图,已知三棱柱
的侧棱与底面垂直,
.
分别是
的中点,点
在直线
上,且
.
;
(2)当
取何值时,直线
与平面
所成角
最大?并求该角取最大值时的正切值.
(3)是否存在点
,使得平面
与平面
所成的二面角的正弦值为
,若存在,试确定点
的位置,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28faa4fb5ac3c67813387512534cbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6429a01a3c89200d73dc49bd70c2d08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597362da92c667625827a89c1c2e3dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ece75fe9b8555909be5a00d2b7af0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
解题方法
【推荐2】如图所示,已知平行六面体
的底面为正方形,
分别为上、下底面的中心,且
在底面
上的射影是
.
(1)求证:平面
平面
;
(2)若点
分别在棱
上,且
,问点
在何处时,
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cef469b1ee29d124cfd6f62423724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/87e148d7-5758-4ac5-abfd-f8c58f75d2b4.png?resizew=274)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2042cecb5b3df38f3025aad09b9188c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d061c7a9c98768ead226c27bdfd2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f166fe0e3f4196b7a34c5ed309a597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1a1fd2fc33e89f357cef772ff6cd0e.png)
您最近一年使用:0次