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对课本一道例题的探究与推广

  • 2026-09-22 11:00:22
对课本一道例题的探究与推广

在立体几何中，空间角与距离的求解几乎离不开法向量．本文从课本的一道平面向量的例题出发，从平面向量推广到空间向量，深入探寻函数及几何与代数这两条主线之间的关联，通过几何直观与代数运算之间的融合，找到求解空间角与距离的另一种通性通法．

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课本里背烂的唐宋八大家,人生结局差距竟这么大!有人安享晚年,有人客死他乡

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  1. CONNECT:[ UseTime:0.000621s ] mysql:host=172.18.0.4;port=3306;dbname=c_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000847s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000413s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000521s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000631s ]
  6. SELECT * FROM `set` [ RunTime:0.000400s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000804s ]
  8. SELECT * FROM `article` WHERE `id` = 471716 LIMIT 1 [ RunTime:0.000344s ]
  9. UPDATE `article` SET `lasttime` = 1790115709 WHERE `id` = 471716 [ RunTime:0.002391s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 66 LIMIT 1 [ RunTime:0.000336s ]
  11. SELECT * FROM `article` WHERE `id` < 471716 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000520s ]
  12. SELECT * FROM `article` WHERE `id` > 471716 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000494s ]
  13. SELECT * FROM `article` WHERE `id` < 471716 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000628s ]
  14. SELECT * FROM `article` WHERE `id` < 471716 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000516s ]
  15. SELECT * FROM `article` WHERE `id` < 471716 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000651s ]
0.090864s