名校
1 . 已知向量
,
,
,若
三个向量共面,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b014d00c7730189d08d0af9ac76f465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62db793887f54878fd020cd5d09811d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9acbd3d31d44fd6b76987baa09d9105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
您最近一年使用:0次
2024-06-05更新
|
101次组卷
|
2卷引用:广东省湛江市第一中学2023-2024学年高二下学期开学考试数学试题
名校
解题方法
2 . 已知矩形ABCD的长与宽的比值为k,
分别为CD的四等分点,现将
沿AF向上翻折,将BCE沿BE向上翻折,使得
,
与四边形ABEF所成角均为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4663fd2fba5440084cd793b67f2f71.png)
时,证明:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)当
时,是否存在P为线段BC上一点,使FP与平面ABD所成角为
,如果存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e496f4e3c850f3515525fd93148fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e496f4e3c850f3515525fd93148fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17fe30d57340c823f3aaa8734fc38d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4663fd2fba5440084cd793b67f2f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f644e851757e3836fe4844659416046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1af463c1192cc6472c70ca84d9bdeb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894706f45d576906aca6acaea15634ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c030b25575d683af91c06e6a3e4f463.png)
您最近一年使用:0次
名校
3 . 如图,在平行六面体
中,
,
,
,
,
,E是
的中点,设
,
,
.
![](https://img.xkw.com/dksih/QBM/2024/2/27/3442137987874816/3442815395504128/STEM/0cf01575e77441be876f6718494246c6.png?resizew=229)
(1)求
的长;
(2)求异面直线
和
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674aa2ce5caabcad5abe65b5402ce6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184359fe3cadc363cf4ebe586c2b3db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2410e0e103cc41264a2d0f5c0e3f3ed4.png)
![](https://img.xkw.com/dksih/QBM/2024/2/27/3442137987874816/3442815395504128/STEM/0cf01575e77441be876f6718494246c6.png?resizew=229)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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4 . 如图,在四棱锥
中,四边形
是菱形,
.
(1)证明:
平面
.
(2)若
,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/e53a4cf54bae1a88c8715b477d70199d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/1403de9c-f94a-47b3-9573-281b0b5b2a29.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1e8e1e47b68cd3014097650121d601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b10f890a5f9bc9140286f8326398d16.png)
您最近一年使用:0次
2024-02-29更新
|
668次组卷
|
2卷引用:广东省2024届高三下学期开学考试数学试题
解题方法
5 . 已知点
是点
在坐标平面
内的射影,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc480968153be39ddeb2979942830a4e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1397a5033e3173000e5d69f7bbef08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d4817aac2a4910300ebca91445eca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc480968153be39ddeb2979942830a4e.png)
您最近一年使用:0次
2024-02-28更新
|
147次组卷
|
2卷引用:广东省中山市迪茵公学2023-2024学年高二下学期开学考试数学试题
6 . 如图,在四棱锥
中,底面
为矩形,
平面
,
,
分别为棱
,
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/9d1d7b1e-e521-4373-8520-8b4633ce1125.png?resizew=153)
(1)证明:
平面
.
(2)求平面
与平面
所成角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee76246dee4f1670e4f21e5eb393b52c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/9d1d7b1e-e521-4373-8520-8b4633ce1125.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
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7 . 由各棱长均相等的四棱柱
截去三棱锥
后得到的几何体如图所示,底面
为正方形,点O为线段
与
的交点,点E为线段
中点,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/8295d89d-9fec-4aa5-a650-b196ec574dd9.png?resizew=195)
(1)证明:
平面
;
(2)若点M为线段
(包含端点)上一点,求
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d236e214b4cb2ed4a914166280c6841.png)
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/8295d89d-9fec-4aa5-a650-b196ec574dd9.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6dcab5d5bdeb695b261e21c8491039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
(2)若点M为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
您最近一年使用:0次
2024-02-24更新
|
520次组卷
|
2卷引用:广东省广州市玉岩中学2023-2024学年高三下学期开学考数学试卷
名校
8 . 已知空间向量
.
(1)计算
和
;
(2)求
与
夹角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3d8e2a1761d761e257ebf8d63df38a.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f0484158c0bb8ef08faf224bba82e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0378850babaf830f1ac2f580c84d43.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2024-02-24更新
|
271次组卷
|
2卷引用:广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题
9 . 已知
为正方体
所在空间内一点,且
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98616ec6a351762039ee41df50060231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
A.![]() |
B.三棱锥![]() |
C.存在唯一的![]() ![]() ![]() |
D.存在唯一的![]() ![]() |
您最近一年使用:0次
2024-01-26更新
|
148次组卷
|
4卷引用:广东省中山市迪茵公学2023-2024学年高二下学期开学考试数学试题
名校
10 . 已知向量
,
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c44f9c2158cd5a0054ed1333da792b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c045c498a8d280b7b97e7169456888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.![]() | B.2 | C.![]() | D.0 |
您最近一年使用:0次
2024-01-24更新
|
131次组卷
|
2卷引用:广东省中山市迪茵公学2023-2024学年高二下学期开学考试数学试题