1 . 在平面直角坐标系中,若直线
过点
,且以
为法向量(与直线方向向量垂直的向量),则直线
上任意一点
满足:
.请你大胆类比猜想:在空间直角坐标系中,若平面
过点
,且以
为法向量,则平面
上任意一点
满足:__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75db25985d446632b3a2675347b08815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e695be0720a683da0e3b41845dc60042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abad325e3ffde67d456a7b50f4ff1da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9d3593fb437c231b62a80b89d07fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c8e1b87cc43d56588c043f68c3c420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
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2 . 在平面几何中,△ABC的边角关系满足余弦定理,
,若四面体中四个面分别是
,
,
,
,其中每两个面之间的二面角的平面角为
,类比三角形中余弦定理得四面体的余弦定理:___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34369422d71dd95c61cdd1b8245d7b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbba1a5994e780dd2b73d1e4947869f.png)
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