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1 . 在长方体
中,
与
和
所成的角均为
,则下面说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 如图,在正四面体
中,
为
中点,
是棱
上的动点,则当异面直线
与
所成角的正弦值最小时,
( )
![](https://img.xkw.com/dksih/QBM/2022/1/5/2869532678864896/2893705660981248/STEM/b8cd9306199c439f884763a9d44fd69d.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdae3c1f3136e7e74d2fbcba051e804b.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f8fe3a5f1f9a2de0cbadd598392ff4.png)
![](https://img.xkw.com/dksih/QBM/2022/1/5/2869532678864896/2893705660981248/STEM/b8cd9306199c439f884763a9d44fd69d.png?resizew=177)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 在空间四边形
中,
分别是
,
,
,
的中点.若
,且
与
所成的角为
,则
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5ef502a7feabf2485b4272587f04ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
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解题方法
4 . 在正方体
中,
是棱AB上的点,且
,G,F分别是棱
,BC的中点,则异面直线
与EF所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/2be09b83-6e1e-4eb6-9a70-39573627cd9a.png?resizew=156)
![](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/ecea6ac9e782b5f11e23b025d5ee195a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e52aed22bcbbd823a5e0b0e9df81c08.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/2be09b83-6e1e-4eb6-9a70-39573627cd9a.png?resizew=156)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 如图,在空间四边形
中,两条对角线
,
互相垂直,且长度分别为4和6,平行于这两条对角线的平面与边
,
,
,
分别相交于点
,
,
,
,记四边形
的面积为
,设
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e096e8740ee7f45b5fbde5d8c1ea6b5e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/d3cbb716-1c89-4e67-8f26-cb8dcbc4b3cc.png?resizew=145)
A.函数![]() ![]() | B.函数![]() |
C.函数![]() ![]() | D.函数![]() ![]() |
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真题
名校
6 . 已知平面α与β所成锐二面角的平面角为
,P为α,β外一定点,过点P的一条直线与α和β所成的角都是
,则这样的直线有且仅有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391479c151307826c9765a47a5f10503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
A.1条 | B.2条 | C.3条 | D.4条 |
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7 . 在正方体
中,过点D作直线l与异面直线AC和
所成角均为
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 在三棱柱
中,已知
,
平面
,则下列选项中,能使异面直线
与
相互垂直的条件为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
A.![]() | B.![]() |
C.四边形![]() | D.四边形![]() |
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4卷引用:湖北省武汉市江夏一中、汉阳一中2019-2020学年高三下学期4月联考理科数学试题
9 . 如图,在底面为正方形,侧棱垂直于底面的四棱柱
中,
,若异面直线
与
所成角的余弦值为
,则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/0b775447-ec7d-4118-b43e-032248955840.png?resizew=103)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f558992e649b93ee36f37513781311a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6df10d0b03d6f6e640d9c5f3695a4e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/0b775447-ec7d-4118-b43e-032248955840.png?resizew=103)
A.3 | B.![]() | C.2 | D.![]() |
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10 . 在长方体
中,
,
为底面矩形
两条对角线的交点,若异面直线
与
所成的角为
,则长方体
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06662eecbf8a7d5581c2ffc70d8096d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2176a388502a0cfdb89b8457497de7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77820915779fc650627d94ea2995eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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