如图,在三棱柱
中,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/922512b5-32d7-47ba-9675-58c65eeab656.png?resizew=225)
(1)求证:
平面
;
(2)若
,Q是
的重心,直线
与
所成角的余弦值为
,求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140088b0cb73812aa9d523c44559298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/922512b5-32d7-47ba-9675-58c65eeab656.png?resizew=225)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b77aeb8979d77702e15c84acb6c888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
22-23高三上·山东青岛·期中 查看更多[3]
更新时间:2022-11-24 14:59:39
|
相似题推荐
解答题-证明题
|
较易
(0.85)
名校
【推荐1】在如图所示的几何体中,四边形
是正方形,
平面
,
,
、
、
分别为
、
、
的中点,且
.
(1)求证:平面
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39967d6f3aed6ce7b6643787795d451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160ccfe256fc5347daa5e4cc26719512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792123541569536/1793761650565120/STEM/def06393be1f4c55bbd1193f7ef170ef.png?resizew=67)
(1)求证:平面
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792123541569536/1793761650565120/STEM/70d46e967bcd454b98e0731071c45bc9.png?resizew=49)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792123541569536/1793761650565120/STEM/80946b964ddb41a983ca6b92f85930f8.png?resizew=37)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0bd4b30dc777ac9da80f6baa3eb31.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792123541569536/1793761650565120/STEM/52d9f6ae1a04420f85e2dee2fb7e45a6.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792123541569536/1793761650565120/STEM/a47a8c61-f935-40d9-b6c9-c59878cc4024.png)
您最近一年使用:0次
解答题-证明题
|
较易
(0.85)
解题方法
【推荐2】如图,在三棱锥
中,
,
,
,平面
平面
,
、
分别为
、
中点.
(1)求证:
平面
.
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fcc62f1c0536d8f82409e8c8df7beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f45265eaed2ba5fc08f6a112a02cd2.png)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809205164941312/1809324023259136/STEM/03afbba882104b83905c867cf7e2edb8.png?resizew=153)
您最近一年使用:0次
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名校
【推荐3】如图,在直三棱柱
中,
,
,
是
的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/09f0a161-ed12-4699-9af7-a9c0d88f32a3.png?resizew=162)
(1)求证
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求直线
与平面
所成的角的大小
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d56e653a138322672e5c8b5d6db958c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10d461a7c0b86a2f09c2ea17f38260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/09f0a161-ed12-4699-9af7-a9c0d88f32a3.png?resizew=162)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
解答题-问答题
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(0.85)
解题方法
【推荐1】已知棱长为
的正方体
,点
、
分别是
、
的中点,建立适当的空间直角坐标系.
(1)写出
、
的坐标;
(2)求
的值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e816833d2cc66ec93db9c03ebe8f08e2.png)
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【推荐2】如图,在直三棱柱A1B1C1-ABC中,AB⊥AC,AB=AC=2,AA1=4,点D是BC的中点,求异面直线 A1B与C1D所成角的余弦值.
![](https://img.xkw.com/dksih/QBM/2021/3/31/2689901894443008/2691916422111232/STEM/c9253519-b46e-4142-9dc3-7f95cb7e006c.png?resizew=162)
您最近一年使用:0次
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【推荐3】在长方体
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
,
是面对角线
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/119fc77e-3b2c-4013-9c5c-36869ce834a0.png?resizew=227)
(1)求证:
;
(2)设异面直线
与
所成角的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9555af092dd58b16d619691164e81114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3017d88fcf32f55d2cfa60164599fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/119fc77e-3b2c-4013-9c5c-36869ce834a0.png?resizew=227)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c497b3188953ea50e4ed889153d63584.png)
(2)设异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
您最近一年使用:0次
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名校
【推荐1】如图,在直三棱柱
中,
,点
分别在棱
和棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/b0bcc5b7-becb-4643-beb1-b3b002a68d18.png?resizew=138)
(1)设
为
中点,求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915b20181d7228b1c9526cbe41f25f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4300bcc3714953bb07e6dbc9e50d5250.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/b0bcc5b7-becb-4643-beb1-b3b002a68d18.png?resizew=138)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383bc7dd1960c2892a37ec0a90119556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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解答题-作图题
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【推荐3】如图,在正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/13/2957152328540160/2957862792085504/STEM/7a18391e-c138-42a1-9ae2-83e658892339.png?resizew=172)
(1)过点
作出一条与平面
平行的直线,并说明理由;
(2)求直线
与平面
所成角的正弦值.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/13/2957152328540160/2957862792085504/STEM/7a18391e-c138-42a1-9ae2-83e658892339.png?resizew=172)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次