如图,四棱柱
中,底面
是矩形,
,
,
,且二面角
的平面角的大小为60°,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/7/2694724598448128/2730857647800320/STEM/370e9f6c-02ae-451b-9de2-62c4497ddab0.png?resizew=313)
(Ⅰ)求证:
;
(Ⅱ)求
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bae5a8b08bcc9e4aa066ed334417f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879c1c9b9650394b4eb4f9badd9d0dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9977da109ae8644f94b286ccded8cc2.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/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/4/7/2694724598448128/2730857647800320/STEM/370e9f6c-02ae-451b-9de2-62c4497ddab0.png?resizew=313)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b731c2724383ea2a4432ef5ef06caf8b.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
2021·浙江嘉兴·二模 查看更多[4]
浙江省嘉兴市2021届高三下学期4月教学测试数学试题(已下线)专题12.立体几何与空间向量(解答题)-《2022届复习必备-2021届浙江省高考冲刺数学试卷分项解析》(已下线)第3讲 立体几何中的向量方法(讲)-2022年高考数学二轮复习讲练测(新教材地区专用)(已下线)NO.4 练悟专区——解答题规范练-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)
更新时间:2021-05-28 16:47:01
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图,已知四棱锥
,底面
为平行四边形,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629770401275904/2629812049494016/STEM/6724da6b-d62e-472d-bbc1-204b30139c3b.png?resizew=292)
(1)求证:
;
(2)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/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232bd9725c48c813083300a4e67626ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e5ef2685d320cb6ab128c06d576858.png)
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629770401275904/2629812049494016/STEM/6724da6b-d62e-472d-bbc1-204b30139c3b.png?resizew=292)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,正三棱柱
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f613ec62-56d1-45df-9038-d9c374ed0b08.png?resizew=160)
(1)求证:
平面
;
(2)若
,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f613ec62-56d1-45df-9038-d9c374ed0b08.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e44cb429eea46e7ee4320147192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9961e091f180e964a962adf6916f33c8.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图,多面体
中,四边形
为菱形,
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2022/12/18/3133684338925568/3134944067674112/STEM/d35bf076251e4b118b40a22b6a93803d.png?resizew=243)
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ceffa9073eaad87857467553f556cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b38f3c6f62e4c04db3253525b74240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d552b00c85d1e11ef3ac6b6e06221fa.png)
![](https://img.xkw.com/dksih/QBM/2022/12/18/3133684338925568/3134944067674112/STEM/d35bf076251e4b118b40a22b6a93803d.png?resizew=243)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1cb818977a967130ef41cd3f9f4fc6.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adef2eaf43d5af6e27d779533b26f461.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在三棱柱
中,平面
平面
,
,
,
,且
,
是棱
上的一点.
(1)求证:
;
(2)是否存在点
,使得直线
与平面
所成角的正弦值为
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996680dbe14b8c065efc380afb19a691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19c98253667b5b010c4ef438b431121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/ed7826c5-51be-4268-bf9c-61261499c20a.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e47254747d59b0d5dabe14654f6681.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84aa4a6500f4b3531a23f83421da5c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58b8da82c88b90de32c7ae06bd7b10b.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐1】如图,在直三棱柱
中,
,
,
分别是棱
,
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/c51060b0-aa1d-45e4-9679-ab4e0f14fa95.png?resizew=136)
(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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da13100aeac68b6bd2b25331b54168e.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853b60fafb31cab8f1bec5510bf1c984.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/c51060b0-aa1d-45e4-9679-ab4e0f14fa95.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d8e9f7f70a5d8313a542f4aa84a1d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,直三棱柱
中,AB=BC=CA=2,
若N为AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/71699b9e-e370-438a-acc3-5a16d5bc6df6.png?resizew=171)
(1)求证:
平面
;
(2)求
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/9b04ec038180fa66533f0ccaa83b5ecc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/71699b9e-e370-438a-acc3-5a16d5bc6df6.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9593b5bde2cef14d5ca46973420f62b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9593b5bde2cef14d5ca46973420f62b.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐3】如图,在四棱锥
中,
平面
,
,且
,
,
,
,
,
为
的中点.
(1)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/0585b6c0f156eecf9662b9846d4eb693.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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/fb314fe1-cea2-4283-b383-8626b4d01d2f.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a041e768d10a0d59d95e1bbef881261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次