µÚÒ»·¶ÎÄÍø - רҵÎÄÕ·¶ÀýÎĵµ×ÊÁÏ·ÖÏíÆ½Ì¨

2020½ìºÓÄÏÊ¡Ðí²ý¼ÃԴƽ¶¥É½¸ßÈýµÚ¶þ´ÎÖÊÁ¿¼ì²âÊýѧ(Àí)ÊÔÌâ(½âÎö°æ)

À´Ô´£ºÓû§·ÖÏí ʱ¼ä£º2025/5/29 8:36:22 ±¾ÎÄÓÉloading ·ÖÏí ÏÂÔØÕâÆªÎĵµÊÖ»ú°æ
˵Ã÷£ºÎÄÕÂÄÚÈݽö¹©Ô¤ÀÀ£¬²¿·ÖÄÚÈÝ¿ÉÄܲ»È«£¬ÐèÒªÍêÕûÎĵµ»òÕßÐèÒª¸´ÖÆÄÚÈÝ£¬ÇëÏÂÔØwordºóʹÓá£ÏÂÔØwordÓÐÎÊÌâÇëÌí¼Ó΢ÐźÅ:xxxxxxx»òQQ£ºxxxxxx ´¦Àí£¨¾¡¿ÉÄܸøÄúÌṩÍêÕûÎĵµ£©£¬¸ÐлÄúµÄÖ§³ÖÓëÁ½⡣

?3??2??2?£¬ Vn?1?Vn?Vn?1?3??3??3??3??2??2??2?µü¼ÓµÃ£ºV£¬ ?V?V?????V?V?V?V123n?1n1n?122?2?. Ôò6?n?1??Vn?12£¬Vn?6n?6?2?11ÓÖV£¬ n?Vn?1?Vn?an?2?2an?1?an?6n?6Ôòa3?2a2?a1?6?2£¬

a4?2a3?a2?6?3£¬

¡­¡­

an?2?2an?1?an?6?n?1?£¬

µü¼ÓµÃ£ºan?2?an?1?a2?a1?62?3?4?????n?1?£¬

??n2?3nÔòan?2?an?1?6???2?3?4??????n?1????a2?a1?2?6£¬ 12?3?1Ôòa3?a1??6£¬

222?3?2a4?a3??6£¬

2¡­¡­

n2?3nan?2?an?1??6£¬

2µü¼ÓµÃ£ºan?2?a2?Ôòan?21?22221?2?3?????n?3?1?2?3?????n?????6n£¬ 213?n?n?1??2n?1??n?n?1??6n?9£¬ 124??3Ôòan?n?n?3.

¹Ê´ð°¸Îª£ºn3?n?3. ¡¾µã¾¦¡¿

±¾Ì⿼²éÓÉж¨ÒåÇóÊýÁÐͨÏʽÒÔ¼°µü¼Ó·¨µÄÔËÓ㬿¼²éÂß¼­Ë¼Î¬ºÍ¼ÆËãÄÜÁ¦.

Èý¡¢½â´ðÌâ

17£®VABCÄÚ½ÇA£¬B£¬CµÄ¶Ô±ß·Ö±ðΪa£¬b£¬c£¬ÇÒ3acosC?3csinA?3b.

µÚ 13 Ò³ ¹² 24 Ò³

£¨1£©Çó½ÇA£»

£¨2£©Èôb?1£¬ÑÓ³¤CBÖÁD.ʹBD?Çó¡÷ABEµÄÃæ»ý. ¡¾´ð°¸¡¿£¨1£©

?93 £»£¨2£©616ÇÒCD?4£¬µãEÔÚADÉÏ£¬ÇÒAE?3ED£¬3AB£¬

¡¾½âÎö¡¿£¨1£©¸ù¾ÝÌâÒ⣬ÓÉÕýÏÒ¶¨ÀíµÃ3sinAcosC?3sinCsinA?3sinB£¬ÀûÓÃÓÕµ¼¹«Ê½ºÍÁ½½ÇºÍÓë²îµÄÕýÏÒ¹«Ê½»¯¼òµÃ3sinAsinC?3cosAsinC£¬¼´¿ÉÇó³ö½ÇA£»

£¨2£©ÉèAB?x£¬BD?3x£¬ÔòCB?4?3x£¬VABCÖУ¬ÓÉÓàÏÒ¶¨ÀíÇó³öx?3£¬ÇóµÃS¡÷ABD?Ãæ»ý. ¡¾Ïê½â¡¿ ½â£º£¨1£©Q115¦Ð33£¬´Ó¶øµÃ³ö¡÷ABEµÄBA?BD?sin?ABD??3?3?sin?22643acosC?3csinA?3b£¬

ÓÉÕýÏÒ¶¨Àí¿ÉµÃ£º3sinAcosC?3sinCsinA?3sinB£¬ ÓÖA?B?C?¦Ð£¬¡àB?¦Ð??A?C?£¬ ¡à3sinAcosC?3sinCsinA?3sin?A?C?£¬ ¼´3sinAsinC?3cosAsinC£¬ ¡ß0?C?¦Ð£¬¡àsinC?0£¬¡àtanA?ÓÖ¡ß0?A?¦Ð£¬¡àA?3£¬ 3¦Ð£¬ 6

£¨2£©ÉèAB?x£¬BD?3x£¬ÔòCB?4?3x£¬

ÔÚVABCÖУ¬ÓÉÓàÏÒ¶¨ÀíµÃ4?3x??2¦Ð?x2?12?2?x?1?cos£¬

6µÚ 14 Ò³ ¹² 24 Ò³

½âµÃx?3»òx?µ±x?53£¬ 2553ʱ£¬CB?4?3?3?0. 22¦Ð£¬ 6ËùÒÔx?3£¬BD?3£¬CB?AC?1£¬?ABC?S¡÷ABD?115¦Ð33. BA?BD?sin?ABD??3?3?sin?2264SVABE?393. SVABD?416¡¾µã¾¦¡¿

±¾Ì⿼²éÕýÏÒ¶¨ÀíºÍÓàÏÒ¶¨ÀíµÄÓ¦Óã¬ÒÔ¼°Èý½ÇÐεÄÃæ»ý¹«Ê½£¬»¹Éæ¼°ÓÕµ¼¹«Ê½ºÍÁ½½ÇºÍÓë²îµÄÕýÏÒ¹«Ê½£¬¿¼²é¼ÆËãÄÜÁ¦.

18£®Èçͼ£¬ËÄÀâ×¶P?ABCDÖУ¬²àÃæPADÊDZ߳¤Îª2µÄµÈ±ßÈý½ÇÐÎÇÒ´¹Ö±ÓÚµ×Ãæ

ABCD£¬AB?BC?1AD£¬?BAD??ABC?90?£¬EÊÇPDµÄÖеã. 2

£¨1£©ÇóÖ¤£ºÖ±ÏßCE//Æ½ÃæPAB£»

£¨2£©µãMÔÚÀâPCÉÏ£¬ÇÒ¶þÃæ½ÇM?AB?DµÄÓàÏÒֵΪ

21£¬ÇóÖ±ÏßBMÓëµ×Ãæ7ABCDËù³É½ÇµÄÕýÏÒÖµ.

¡¾´ð°¸¡¿£¨1£©Ö¤Ã÷¼û½âÎö£»£¨2£©23 5¡¾½âÎö¡¿£¨1£©È¡PAÖеãF£¬Á¬½áEF£¬BF£¬¸ù¾ÝÈý½ÇÐÎÖÐλÏßµÄÐÔÖÊ£¬µÃ³öEF//AD£¬

EF?1AD£¬½áºÏÌõ¼þ£¬¿ÉÖ¤³öËıßÐÎBCEFΪƽÐÐËıßÐΣ¬µÃ³öCE//BF£¬×îºó2¸ù¾ÝÏßÃæÆ½ÐеÄÅж¨¶¨Àí£¬¼´¿ÉÖ¤Ã÷Ö±ÏßCE//Æ½ÃæPAB£»

£¨2£©½¨Á¢¿Õ¼äÖ±½Ç×ø±êϵ£¬ÉèPM??PC?0???1?£¬Ôò¿ÉµÃM?,1,3?3?£¬ÓÉͼ¿ÉÖªµ×ÃæABCD·¨ÏòÁ¿£¬¸ù¾Ý¿Õ¼äÏòÁ¿·¨Çó³öÆ½ÃæMABµÄ·¨ÏòÁ¿£¬ÀûÓÃÒÑÖªµÄ¶þÃæ½ÇÓàÏÒÖµ£¬Çó³ö?£¬µÃ³öµãM×ø±ê£¬ÔÙÀûÓÿռäÏòÁ¿ÇóÏßÃæ½ÇµÄ¹«Ê½£¬Çó³öÖ±ÏßBMµÚ 15 Ò³ ¹² 24 Ò³

????Óëµ×ÃæABCDËù³É½ÇµÄÕýÏÒÖµ. ¡¾Ïê½â¡¿

½â£ºÖ¤Ã÷£º£¨1£©È¡PAÖеãF£¬Á¬½áEF£¬BF£¬ ÒòΪEΪPDµÄÖе㣬ËùÒÔEF//AD£¬EF?ÓÉ?BAD??ABC?90?£¬µÃBC//AD£¬ ÓÖBC?1AD£¬ 21AD£¬ËùÒÔEF?BC,EF//BC£¬ 2ÔòËıßÐÎBCEFΪƽÐÐËıßÐΣ¬ÓÐCE//BF£¬

ÓÖBF?Æ½ÃæPAB£¬CE?Æ½ÃæPAB£¬¹ÊCE//Æ½ÃæPAB. £¨2£©

ÓÉÒÑÖªµÃBA?AD£¬ÒÔAÎª×ø±êÔ­µã£¬ABµÄ·½ÏòΪxÖáÕý·½Ïò£¬ABΪµ¥Î»³¤£¬ ½¨Á¢ÈçͼËùʾµÄ¿Õ¼äÖ±½Ç×ø±êϵA?xyz£¬

ÔòA?0,0,0?£¬B?1,0,0?£¬C?1,1,0?£¬P0,1,3£¬

????PC?1,0,?3£¬AB??1,0,0?£¬

ÉèPM??PC?0???1?£¬Ôò¿ÉµÃM?,1,3?3?£¬ ÉèÆ½ÃæMABµÄÒ»¸ö·¨ÏòÁ¿Îªm??x,y,z?£¬

?????????vruuux?0??m?AB?0?vÔò?ruuuu£¬¼´?£¬

??m?AM?0??x?y?3?1???z?0È¡z?1£¬Ôòm?0,3??3,1£¬

???µÚ 16 Ò³ ¹² 24 Ò³

2020½ìºÓÄÏÊ¡Ðí²ý¼ÃԴƽ¶¥É½¸ßÈýµÚ¶þ´ÎÖÊÁ¿¼ì²âÊýѧ(Àí)ÊÔÌâ(½âÎö°æ).doc ½«±¾ÎĵÄWordÎĵµÏÂÔØµ½µçÄÔ£¬·½±ã¸´ÖÆ¡¢±à¼­¡¢ÊղغʹòÓ¡
±¾ÎÄÁ´½Ó£ºhttps://www.diyifanwen.net/c8a3as7l8qu5a66i6tmib553973044s010aw_4.html£¨×ªÔØÇë×¢Ã÷ÎÄÕÂÀ´Ô´£©

Ïà¹ØÍÆ¼ö£º

ÈÈÃÅÍÆ¼ö
Copyright © 2012-2023 µÚÒ»·¶ÎÄÍø °æÈ¨ËùÓÐ ÃâÔðÉùÃ÷ | ÁªÏµÎÒÃÇ
ÉùÃ÷ :±¾ÍøÕ¾×ðÖØ²¢±£»¤ÖªÊ¶²úȨ£¬¸ù¾Ý¡¶ÐÅÏ¢ÍøÂç´«²¥È¨±£»¤ÌõÀý¡·£¬Èç¹ûÎÒÃÇ×ªÔØµÄ×÷Æ·ÇÖ·¸ÁËÄúµÄȨÀû,ÇëÔÚÒ»¸öÔÂÄÚ֪ͨÎÒÃÇ£¬ÎÒÃǻἰʱɾ³ý¡£
¿Í·þQQ£ºxxxxxx ÓÊÏ䣺xxxxxx@qq.com
ÓåICP±¸2023013149ºÅ
Top