解题方法
1 . 在四棱锥
中,
平面
,且底面
为边长为2的菱形,
,
.
(1)记
在平面
内的射影为
(即
平面
),试用作图的方法找出M点位置,并写出
的长(要求写出作图过程,并保留作图痕迹,不需证明过程和计算过程);
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/4d27cde3-f8e6-4443-85a2-eb3bd7168a7b.png?resizew=191)
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a46dc0bb5d8fa33583817e530a5d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/4d27cde3-f8e6-4443-85a2-eb3bd7168a7b.png?resizew=191)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
2 . 如图,在长方体
中,
,
,
为
的中点
(1)在所给图中画出平面
与平面
的交线(不必说明理由)
(2)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef676509065322bfc244e59607bb60d.png)
(3)求平面
与平面
所成锐二面角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/90a20a4f-b105-4e81-a597-ec7f8158ad82.png?resizew=158)
(1)在所给图中画出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028856d5101687dd8eaf130846489cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef676509065322bfc244e59607bb60d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f511b6f2e0072ff616a5b79b0617db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef676509065322bfc244e59607bb60d.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028856d5101687dd8eaf130846489cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef676509065322bfc244e59607bb60d.png)
您最近一年使用:0次
3 . 如图,长方体
中,
,
,点
,
,
分别为
,
,
的中点,过点
的平面
与平面
平行,且与长方体的面相交,交线围成一个几何图形.
![](https://img.xkw.com/dksih/QBM/2018/3/3/1894140104613888/1896558688067584/STEM/399fbedd425043aeab4693937d775e44.png?resizew=155)
(1)在图中画出这个几何图形(说明画法,不需要说明理由);
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://img.xkw.com/dksih/QBM/2018/3/3/1894140104613888/1896558688067584/STEM/399fbedd425043aeab4693937d775e44.png?resizew=155)
(1)在图中画出这个几何图形(说明画法,不需要说明理由);
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432b602bbaf82a4a40091ecfc8a8ffb0.png)
您最近一年使用:0次