名校
1 . 如图,正方形
中,
分别为线段
上的点,满足
,连接
交于点
.
;
(2)设
,求
的最大值和
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f8eebda19eded2b059774a8c2666c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9bfb96c6a7b5bf01bb15042355ac215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f49d1de7c6dfc04b6e84e23eec0a1d7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8979e5728aef6fa57b6970525afcb6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a61103ea69687ba91d5b380c0e2238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d6a99033826bd1b44f58b9e11ff52e.png)
您最近一年使用:0次
2024-04-11更新
|
408次组卷
|
2卷引用:湖北省十四校协作体2023-2024学年高一下学期3月质量检测数学试卷
名校
解题方法
2 . 如图,已知斜三棱柱
中,平面
平面
,
与平面
所成角的正切值为
,所有侧棱与底面边长均为2,D是边AC中点.
(1)求证:
∥平面
;
(2)求异面直线
与
所成的角;
(3)F是边
一点,且
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/30/1c05cdba-2179-49f6-b923-bc0f589b7092.png?resizew=204)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(3)F是边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4633c8d720b79fbd51094e000fd53a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e57df2381ec2af9a8516a9fa28b695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-06-28更新
|
887次组卷
|
2卷引用:湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期第一次月考数学试题
名校
3 . 已知向量
,且向量
与
共线.
(1)证明:
;
(2)求
与
夹角的余弦值;
(3)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530c1a9b7586e6e7f3f9377a6f2f0881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1c5bcaa260128e281a12f6ef6aacbc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20f69af6870bada879cddd7f6794d24.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f5cb84750e467daf59bbeebd0738d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-03-21更新
|
839次组卷
|
4卷引用:湖北省宜昌英杰学校2022-2023学年高一下学期5月月考数学试题
4 . 在直角坐标系中,已知四边形ABCD的四个顶点坐标为
,
,
,
,过原点O的直线EF交AB,CD于E,F点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/976a6a3c-e6f4-4720-a267-33ed81cdf29d.png?resizew=177)
(1)求证:F是线段CD中点;
(2)求向量
与向量
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993769b494e12c21dff0ee7c53a4a49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ce8d4a9d432afe03a988ae2d49c28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56286216c1c313e19f4a196fcaba6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bc3549df1b009f8c95eab6a2b0c572.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/976a6a3c-e6f4-4720-a267-33ed81cdf29d.png?resizew=177)
(1)求证:F是线段CD中点;
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ed9c2e9fabbfc63733bae8fa079d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
您最近一年使用:0次
5 . 在平面直角坐标系内,已知
,
),
.
(I)若
,求证
为直角三角形.
(Ⅱ)若
,求实数λ、t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87702ca4e2800e2063867819e6101748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69be470227445b84e0ff57e07f17a229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9096aa9154ca32f3d5a947cc72b88fc5.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948cb5cb3919d7250ff1191e6b9052a5.png)
您最近一年使用:0次