已知直线
的方向向量为
,平面
的法向量为
,则直线与平面夹角的余弦值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69e08f2a9bb8f6ed36b6abc054b8a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f916a717eb00945791c88399810757a.png)
更新时间:2021-02-28 14:30:16
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【知识点】 线面角的向量求法
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解题方法
【推荐1】在三棱锥
中,
两两垂直,
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,
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的中点,
为
的中点,则
与平面
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较易
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解题方法
【推荐2】已知三棱锥
中,
两两垂直,
,则直线
与平面
所成的角的正弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c83984c62d390c6b30efa5d4e560de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293ceeff647cee19dd018ea44c2a947b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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