如图,在三棱柱
中,侧面
与侧面
都是菱形,
,
.记
.
(1)用
表示
,并证明
;
(2)若
为棱
的中点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab724e71a5c81257dbcc970ae4e087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcc3114ae5565f7414363d3626649bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7b92264c6a0e4be7dc1e494c6f1dc3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/c7945335-de3f-4676-b2a5-8f54e115e324.png?resizew=160)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb0dbfda18f5cf552c4b38a2527a20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faac7a82235d53bb4b6abe7ee54951.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
23-24高二上·河南焦作·期中 查看更多[2]
更新时间:2023-11-26 22:43:11
|
相似题推荐
解答题-问答题
|
较易
(0.85)
名校
【推荐1】如图,在平行六面体
中,
,
,
,
,
.求:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/b2620ea4-59ee-423e-a824-dfa413ecf7b8.png?resizew=183)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c456f8531a93c8d43790b744422c8ca.png)
(2)
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5600c2061f6e12991bf271a4a3ab51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037bba27008abc96a6dba99753549ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcf6a87fd2d2034aab93631a4a4ac5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/b2620ea4-59ee-423e-a824-dfa413ecf7b8.png?resizew=183)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c456f8531a93c8d43790b744422c8ca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
您最近一年使用:0次
解答题-问答题
|
较易
(0.85)
名校
解题方法
【推荐2】如图,正四面体ABCD(所有棱长均相等)的棱长为1,E,F,G,H分别是正四面体ABCD中各棱的中点,设
,
,
,试采用向量法解决下列问题:
(1)求
的模长;
(2)求
,
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f111250ea56c59b179cfc7b5db12cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/12/2ae55861-e7c0-4a16-8bac-8e9b6fec1050.png?resizew=165)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21162e18e3c389215ac1a44858d6c5a7.png)
您最近一年使用:0次
解答题-问答题
|
较易
(0.85)
名校
【推荐1】如图,在四棱锥
中,底面ABCD是边长为1的正方形,侧棱PA的长为2,且PA与AB、AD的夹角都等于60°,M是PC的中点,设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/6907a61d-72da-4c9f-a805-06718c836cea.png?resizew=172)
(1)试用
表示向量
;
(2)求BM的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e28eb023fe260d9b50fcc441e1df95e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/6907a61d-72da-4c9f-a805-06718c836cea.png?resizew=172)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96022a881e03e32d3483d997c3f170c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4648d56ec5ba86c288bc22737250ba0.png)
(2)求BM的长.
您最近一年使用:0次
解答题-问答题
|
较易
(0.85)
【推荐2】已知在直三棱柱中,
,
,建立适当的空间直角坐标系,求向量
,
,
的坐标.
您最近一年使用:0次
解答题-问答题
|
较易
(0.85)
名校
【推荐1】如图,直三棱柱
中,
,
,
为棱AB的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/f9f0e52a-7b1d-466d-801e-1cd096a3e7cf.png?resizew=185)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483678f653daf513747f27f3dd6acf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/f9f0e52a-7b1d-466d-801e-1cd096a3e7cf.png?resizew=185)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06947327f4c41340b8713e8a6b4c87.png)
您最近一年使用:0次
解答题-问答题
|
较易
(0.85)
名校
【推荐2】如图,在长方体
中,
,
,点E在棱AB上移动.
(1)证明:
;
(2)求平面
的法向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/25/31f96c09-ee25-4bc4-8451-c3dbfb4a38f7.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa81c1f81266b4ef3d471bc6bfc38d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
解答题-证明题
|
较易
(0.85)
【推荐3】已知平行六面体
中,底面是边长为
的正方形,侧棱长为2,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/6dadc358-ca61-497f-abd6-473da2020296.png?resizew=181)
(1)求证:
;
(2)求异面直线
与
所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce64c7cf095a20894e9ddd0d95992a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/6dadc358-ca61-497f-abd6-473da2020296.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c02ffbf0d9a3a73b896732082710c2f.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次