2023高三·全国·专题练习
1 . 证明正三棱柱
中,若
时,则
与
就不可能垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e94f7092a1af99d279ff0daa5035f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
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2 . 已知两条异面直线a,b所成角为
,距离为d,两直线上分别取点E、F.
,
,M、N分别为公垂线与a、b的交点,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411768ff69e9034dd487de83f7ea97c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2763fdfc8ee8b0efaf2f1b1c181ffa7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1bb6beca539b2aad1a04b93ff58bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c577c79eacdb7e00270704e5c0336bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee975978fd2a3d73a3ba8e2f8ac99fa.png)
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解题方法
3 . 如图,在等腰直角
中,
,D为
中点,E,F分别为
,
中点.现将
绕边
翻折至
,使面
面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9a784e43-853f-40c3-8cbf-fcb9f7d591e5.png?resizew=285)
(1)证明:
平面
;
(2)若Q是线段
上的动点,求当
与
所成角取得最小值时,线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2e679d7b314ff58c284da08e8edbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/9a784e43-853f-40c3-8cbf-fcb9f7d591e5.png?resizew=285)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若Q是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632917e61f4208959686d118c7f19231.png)
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