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共回答了22个问题采纳率:95.5% 举报
(Ⅰ)
![](https://img.yulucn.com/upload/0/e0/0e070d0feb92fdfcfa9214e6b03071a6_thumb.jpg)
;(Ⅱ)
(I)可以利用体积法求解,根据
![](https://img.yulucn.com/upload/b/d5/bd586f2431ec28abaf60a5a0dc04394b_thumb.jpg)
.也可利用向量法.
(II)可以考虑向量法,建系后,求出二面角两个面的法向量,然后求出法向量的夹角,再根据法向量的夹角与二面角相等或互补求解.
(Ⅰ)以
![](https://img.yulucn.com/upload/4/d0/4d0f8a77e4d52a742e032879f51fb415_thumb.jpg)
为坐标原点,射线
![](https://img.yulucn.com/upload/4/50/45047ce731eac4e66b4a23aba8751851_thumb.jpg)
分别为
![](https://img.yulucn.com/upload/0/81/0811f00355a4fb85898fc5b7df2b39f6_thumb.jpg)
轴、
![](https://img.yulucn.com/upload/0/1f/01fbd6d7921796ab93dd053b7d9bd4f6_thumb.jpg)
轴、
![](https://img.yulucn.com/upload/9/de/9de50b3febd356008f1ca9a6ab33a444_thumb.jpg)
轴正半轴,建立空间直角坐标系
![](https://img.yulucn.com/upload/b/61/b61f2a76cac94510e581814351e0ed15_thumb.jpg)
,设
![](https://img.yulucn.com/upload/8/99/899a3493853fe7a2d2491ee98143d1e5_thumb.jpg)
,则
![](https://img.yulucn.com/upload/c/a4/ca416d598cc4d76e27a0bb452a506888_thumb.jpg)
,
![](https://img.yulucn.com/upload/f/a2/fa2bdb7d9d4a952626b5554893b0cb7c_thumb.jpg)
,
![](https://img.yulucn.com/upload/0/60/06040e64c55423371775bfc0ad580625_thumb.jpg)
,
![](https://img.yulucn.com/upload/7/27/727cbb5a84b5500cf3d14a71179e3fb6_thumb.jpg)
.因此
![](https://img.yulucn.com/upload/c/5a/c5ad0a5580ca0b0112ab52016d30bb9f_thumb.jpg)
),
![](https://img.yulucn.com/upload/4/30/430357b0096038f5a0c5f68fcd882780_thumb.jpg)
,
![](https://img.yulucn.com/upload/c/df/cdf566b67e53dd9292b928b39932755f_thumb.jpg)
.
则
![](https://img.yulucn.com/upload/3/84/3840fef4b88b7b213e90a746aec4b98c_thumb.jpg)
,所以
![](https://img.yulucn.com/upload/a/df/adf6411bfcc630d319eedb23dda4af64_thumb.jpg)
⊥平面
![](https://img.yulucn.com/upload/a/f4/af4edbc60b73a74bf8f06b149152db45_thumb.jpg)
.又由
![](https://img.yulucn.com/upload/9/66/966649f73a942f749d50704c74524edc_thumb.jpg)
∥
![](https://img.yulucn.com/upload/5/fd/5fd06b38ca83ca8798449fe94c4eeb38_thumb.jpg)
知
![](https://img.yulucn.com/upload/9/66/966649f73a942f749d50704c74524edc_thumb.jpg)
∥平面
![](https://img.yulucn.com/upload/a/f4/af4edbc60b73a74bf8f06b149152db45_thumb.jpg)
,故点
![](https://img.yulucn.com/upload/d/f8/df8c6332df9b9f18fc3106c226370283_thumb.jpg)
到平面
![](https://img.yulucn.com/upload/a/f4/af4edbc60b73a74bf8f06b149152db45_thumb.jpg)
的距离为点
![](https://img.yulucn.com/upload/4/d0/4d0f8a77e4d52a742e032879f51fb415_thumb.jpg)
到平面
![](https://img.yulucn.com/upload/a/f4/af4edbc60b73a74bf8f06b149152db45_thumb.jpg)
的距离,即为
![](https://img.yulucn.com/upload/0/ce/0ced4a5acd06d1fb4a5bdfd9444d7d2a_thumb.jpg)
…(6分)
(Ⅱ)因为
![](https://img.yulucn.com/upload/5/00/500e216c8eac830c9807972adecea097_thumb.jpg)
,则
![](https://img.yulucn.com/upload/6/5d/65dcca0ed1a82faf9eb0c3bc3c0a427e_thumb.jpg)
.设平面
![](https://img.yulucn.com/upload/f/ee/feeb11e903d53d32ef7b799e94dada15_thumb.jpg)
的法向量
![](https://img.yulucn.com/upload/2/d1/2d1673e3f0483cb3d882d3c9caf2d3e2_thumb.jpg)
,则由
![](https://img.yulucn.com/upload/9/e2/9e2b07bf6f786fa87a5f960e8773d801_thumb.jpg)
可解得:
![](https://img.yulucn.com/upload/e/8e/e8ebbba1e4febc6f894c24cfe39b8e67_thumb.jpg)
,同理可解得
平面
![](https://img.yulucn.com/upload/5/67/56762be83891eb4e1282467ce3c5a75c_thumb.jpg)
的法向量
![](https://img.yulucn.com/upload/c/34/c3455dc9c8afd0e26c578808a06e68b7_thumb.jpg)
,故
所以二面角
![](https://img.yulucn.com/upload/3/5f/35f764165d9948dfe32fab0c0b175666_thumb.jpg)
1 的平面角的余弦值为
![](https://img.yulucn.com/upload/5/2e/52e4adee4cc33de9a643a6909a0c9b30_thumb.jpg)
. ……(12分)
注:此
1年前
1