如图,在四棱锥P—ABCD中,底面ABCD为正方形,PA⊥底面ABCD,PA=AB,E为线段PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/1892d0ea-50bc-44a0-8a44-a71261c9fc4e.png?resizew=165)
(1)若F为线段BC的中点,求异面直线EF与PD所成角的余弦值;
(2)证明:点F在线段BC上移动时,△AEF始终为直角三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/1892d0ea-50bc-44a0-8a44-a71261c9fc4e.png?resizew=165)
(1)若F为线段BC的中点,求异面直线EF与PD所成角的余弦值;
(2)证明:点F在线段BC上移动时,△AEF始终为直角三角形.
更新时间:2020-08-05 20:11:41
|
相似题推荐
【推荐1】如下图,在四棱锥
中,底面
是边长为2的正方形,
与
相交于点O,E为
的中点,
,
,
与平面
的交线为l,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4256783d83d326a3279ecf9821d2a2.png)
(2)证明:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f84e995fae3d235a050d29d5f271f1c.png)
平面
;
(3)当点A到平面
的距离最大时,求侧面
与底面
所成二面角的大小.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14f698605a196cf83ccba6a601d0e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0921a2db64d89d1d27d4228c4a438a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f84e995fae3d235a050d29d5f271f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4256783d83d326a3279ecf9821d2a2.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f84e995fae3d235a050d29d5f271f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)当点A到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
解题方法
【推荐2】如图,在三棱锥
中,
面
,
,
,
为线段
的中点,
为线段
上一点.
![](https://img.xkw.com/dksih/QBM/2021/12/6/2866745284509696/2868074143653888/STEM/9f3e1089-9ab8-4b12-bbc4-1ff8b5f2ab9e.png?resizew=176)
(1)求
与
所成角;
(2)当
平面
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2021/12/6/2866745284509696/2868074143653888/STEM/9f3e1089-9ab8-4b12-bbc4-1ff8b5f2ab9e.png?resizew=176)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐1】如图,在四棱锥中,
,四边形
是菱形,
是棱
上的动点,且
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99a9bfe6e74558b2129cbccc6f6a776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐2】如图,在四棱锥
中,
平面ABCD,
,
,
,E为PB的中点,______.
![](https://img.xkw.com/dksih/QBM/2021/11/30/2862481177198592/2863814632972288/STEM/de6da304-f744-40c8-976d-5159448ef04e.png?resizew=223)
从①
;②
平面PAD这两个条件中选一个,补充在上面问题的横线中,并完成解答.
注:如果选择多个条件分别解答按第一个解答计分.
(1)求证:四边形ABCD是直角梯形.
(2)求直线AE与平面PCD所成角的正弦值.
(3)在棱PB上是否存在一点F,使得
平面PCD?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1720da6d65e7fa854d98322d3864240.png)
![](https://img.xkw.com/dksih/QBM/2021/11/30/2862481177198592/2863814632972288/STEM/de6da304-f744-40c8-976d-5159448ef04e.png?resizew=223)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa1162d5481e2441fe5bc0d49a576b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
注:如果选择多个条件分别解答按第一个解答计分.
(1)求证:四边形ABCD是直角梯形.
(2)求直线AE与平面PCD所成角的正弦值.
(3)在棱PB上是否存在一点F,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcd55ad87acd31ce56136e0c11ed300.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐3】如图,在四棱锥P—ABCD中,
,
是等腰直角三角形,且
.
![](https://img.xkw.com/dksih/QBM/2020/7/14/2505773335322624/2507243351056384/STEM/abc14f47-24ed-4693-8064-51f593bab5c1.png)
(1)求证: AD⊥BP;
(2)求直线BC与平面ADP所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b3c33cb3ec70d63c26b8fc8d4ce6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8620d64b7e086abc59a8f7ba88ee27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948b17e6397228ab1605526c203b711a.png)
![](https://img.xkw.com/dksih/QBM/2020/7/14/2505773335322624/2507243351056384/STEM/abc14f47-24ed-4693-8064-51f593bab5c1.png)
(1)求证: AD⊥BP;
(2)求直线BC与平面ADP所成角的正弦值.
您最近一年使用:0次