1 . (1)已知
,且
,求x,y,z所要满足的关系式;
(2)已知
,求一个非零空间向量
,使得
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb836776d0289369bd8d4b2899d7487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b958a367fa2f08b6202a5a6ebf5e9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81612ffb48076f748c702d031b5210ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924007c7c9a513a8404b937cbcb958f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a004ff242e134f164009d475f4d4e999.png)
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21-22高二·湖南·课后作业
2 . (1)设
,
分别是不重合的直线
,
的方向向量,判断
,
的位置关系.
①
,
;
②
,
.
(2)设
,
分别是两个不同的平面
,
的法向量,判断
,
的位置关系.
①
,
;
②
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cfc1cefe7b67fb229ab9e401469d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e2d5605b90809709ee90ac67ce9ae2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9653bb37520d76ee6fa6ebba221daf9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b00244a2319d1ee2ba150688f591608.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b268bd72d3067d422b5f368f5cfda3c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623e653171a8553b8cd94b9868fbac67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891947af5a6cfe8fb721c5234f118771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee32ab7bf0f122bf6f71338dbb8b2a56.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cc049192dc9b2fc817bdc7dcfabf77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c6834a01b2878c820f7f53c7c37aeb.png)
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21-22高二·湖南·课后作业
3 . 阅读“多知道一点:平面方程”,并解答下列问题:
(1)建立空间直角坐标系,已知
,
,
三点,而
是空间任意一点,求A,B,C,P四点共面的充要条件.
(2)试求过点
,
,
的平面ABC的方程,其中a,b,c都不等于0.
(3)已知平面
有法向量
,并且经过点
,求平面
的方程.
(4)已知平面
的方程为
,证明:
是平面
的法向量.
(5)①求点
到平面
的距离;
②求证:点
到平面
的距离
,并将这个公式与“平面解析几何初步”中介绍的点到直线的距离公式进行比较.
(1)建立空间直角坐标系,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f6f9d8550d619061ab0ba1105ec6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf322f683d50ecd3c7d4d5996122726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
(2)试求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3ea554707fa3fc12fc9de51c94e4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5622d4be6bba8c7a6851dc082ef34fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1f4b53c90e4c31dd35b4bb548c5193.png)
(3)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b163c34a920cb649829c376e7870007a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(4)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e0ae1c14104ee9985e3ba31c604531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(5)①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae715c996c1a6b5e35a3807c671bd6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
②求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e874a5821372c21a768cd1f5e20536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c828e62664e7373ed1f6dde8aa9653c.png)
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21-22高二·湖南·课后作业
4 . 如图,正方体
的棱长等于
,
为正方形
的中心,
、
分别为棱
、
的中点.试判断下列结论是否成立,并说明理由.
;
(2)
;
(3)
;
(4)
为直角三角形;
(5)
的面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486e6c5f576d4539be7e29ca98bee66e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f98d683e9dc7c210890e4f7220e9c1.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a23e3ec9297b3722856590ad6c510a.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e8acea56a9f17e6ef9bbce1633497f.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e8acea56a9f17e6ef9bbce1633497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
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21-22高二·全国·课后作业
5 . 已知
,
.
(1)写出一个向量
的坐标,使得
;
(2)写出一个向量
的坐标,使得
;
(3)写出与坐标平面垂直的一个向量的坐标;
(4)写出与坐标平面
平行的两个互不平行的向量的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f832041816027c2cc22a1180d4d5161f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5752dc52c601a54f274879d7835a0fa.png)
(1)写出一个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff6eb1f956257db452baac0201b4c86.png)
(2)写出一个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eec20ed75c3a6f25cd9e63d66403840.png)
(3)写出与坐标平面垂直的一个向量的坐标;
(4)写出与坐标平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
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2022-03-05更新
|
167次组卷
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3卷引用:3.2 空间向量运算的坐标表示及应用
(已下线)3.2 空间向量运算的坐标表示及应用北师大版(2019)选择性必修第一册课本习题第三章3.2空间向量运算的坐标表示及应用北师大版(2019)选择性必修第一册课本例题3.2 空间向量运算的坐标表示及应用
6 . 填空:
(1)若直线
的方向向量为
,
的方向向量为
,则
与
的位置关系是______ .
(2)若
,
分别是平面
,
的法向量,则平面
,
的位置关系是______ .
(3)若直线
的方向向量为
,平面
的法向量为
,则直线
与平面
的位置关系是______ .
(4)已知直线
的方向向量为
,平面
的法向量为
.若
,则实数
的值为______ .
(5)设
,
分别是平面
,
的法向量.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ .
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b36554d98cc5ce584adb04209ece057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f809d831dc22c0dcafc964b06c2975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7cdc1e1dcfc0d7e563d8b2937867c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f6c9c540cd4c4f0ece86bea273167b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dd1ca2fa57df9103400bec3b146dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e63fedeb399e0a6a82e097aaf6d558e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(4)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d2ae9371e3f5a1bd0ec41125a0120e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe585e69833f510440bf8bfcb8b232fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(5)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffb97eea0fca26aa4e0aff344ed6764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fac57ea1c1d9db0810449a5b402a205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b303b1f07604f5303aea94df7f0518e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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2021-12-10更新
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2卷引用:苏教版(2019) 选修第二册 名师导学 第六章 6.3.2 空间线面关系的判定