名校
1 . 在空间中,四条不共线的向量
、
、
、
两两间的夹角均为
.则
的大小为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0762365cf0afd8d6966d7d3407e2ade0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
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2016高二·全国·课后作业
2 . 如图,已知
、
、
、
、
、
、
、
、
为空间的
个点,且
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/11/15/1836136229879808/1826268636012544/STEM/2022ebbeb0664162b3f84a7ed49038ac.png?resizew=167)
求证:(1)
、
、
、
四点共面,
、
、
、
四点共面;
(2)
;
(3)
.
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/c8fa5b04e30e48868fe132789b807597.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3066e7be6d7c4c518443aac35ebc6fc5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b91007e2ea5e433e95db20f4365af044.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/97903bb1c17f421d99f9d22a60f06e1a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/04d375abd23446d49614ae0320e80084.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b5a2daa15b914c598c2eab346ad7223e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/33f3cc1423584e0dbcb2758c3e25432d.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0b593aab85fb4dbcb2ebdf05a19793da.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/855db6b1d0d84981842248c6e4474b0e.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0dbdef66d115422081bc2e5a32f48d7c.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/847f57351bde4581abef8a8eca1c6630.png?resizew=72)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/c6b86275082f489cbaca3001edb878c6.png?resizew=74)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/cba340111acb4e49b35a90810589fa18.png?resizew=77)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/ae8730bc42424af6af4187c0829e1322.png?resizew=115)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/f1055c0362da4a4fbde3e599db2ebaeb.png?resizew=116)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3ef175e21b1b4b148b88a747da214799.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/4f3b0d4465694c178a6a044b9be25f3a.png?resizew=42)
![](https://img.xkw.com/dksih/QBM/2016/11/15/1836136229879808/1826268636012544/STEM/2022ebbeb0664162b3f84a7ed49038ac.png?resizew=167)
求证:(1)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3066e7be6d7c4c518443aac35ebc6fc5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b91007e2ea5e433e95db20f4365af044.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/97903bb1c17f421d99f9d22a60f06e1a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/04d375abd23446d49614ae0320e80084.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b5a2daa15b914c598c2eab346ad7223e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/33f3cc1423584e0dbcb2758c3e25432d.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0b593aab85fb4dbcb2ebdf05a19793da.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/855db6b1d0d84981842248c6e4474b0e.png?resizew=19)
(2)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/EXPLANATION/8fe0f5e54a904f04abfa0fdf835415be.png?resizew=68)
(3)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/26aac0e0723242a8984e34736049ce88.png?resizew=76)
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