ÔÆÌ⺣ - רҵÎÄÕ·¶ÀýÎĵµ×ÊÁÏ·ÖÏíÆ½Ì¨

µ±Ç°Î»ÖãºÊ×Ò³ > Æ½ÃæÏòÁ¿ÖªÊ¶µã×ܽá

Æ½ÃæÏòÁ¿ÖªÊ¶µã×ܽá

  • 62 ´ÎÔĶÁ
  • 3 ´ÎÏÂÔØ
  • 2025/7/12 4:25:30

¸ßÖÐÊýѧ±ØÐÞ4 Æ½ÃæÏòÁ¿

֪ʶµã¹éÄÉ

Ò».ÏòÁ¿µÄ»ù±¾¸ÅÄîÓë»ù±¾ÔËËã

1ÏòÁ¿µÄ¸ÅÄ

???¢ÙÏòÁ¿£º¼ÈÓдóСÓÖÓз½ÏòµÄÁ¿ÏòÁ¿Ò»°ãÓÃa,b,c¡­¡­À´±íʾ£¬»òÓÃÓÐÏòÏß¶ÎµÄÆðµãÓëÖÕ

µãµÄ´óд×Öĸ±íʾ£¬È磺AB¼¸ºÎ±íʾ·¨ AB£¬a£»×ø±ê±íʾ·¨a?xi?yj?(x,y) Ïò

??Á¿µÄ´óС¼´ÏòÁ¿µÄÄ££¨³¤¶È£©£¬¼Ç×÷|AB|¼´ÏòÁ¿µÄ´óС£¬¼Ç×÷£üa£ü

?ÏòÁ¿²»ÄܱȽϴóС£¬µ«ÏòÁ¿µÄÄ£¿ÉÒԱȽϴóС£®

????0ÓëÈÎÒâÏòÁ¿Æ½ÐÐÁãÏòÁ¿a£½0?£ü¢ÚÁãÏòÁ¿£º³¤¶ÈΪ0µÄÏòÁ¿£¬¼ÇΪ0£¬Æä·½ÏòÊÇÈÎÒâµÄ£¬

?a£ü£½0 ÓÉÓÚ0µÄ·½ÏòÊÇÈÎÒâµÄ£¬Çҹ涨0ƽÐÐÓÚÈκÎÏòÁ¿£¬¹ÊÔÚÓйØÏòÁ¿Æ½ÐУ¨¹²Ïߣ©

µÄÎÊÌâÖÐÎñ±Ø¿´Çå³þÊÇ·ñÓС°·ÇÁãÏòÁ¿¡±Õâ¸öÌõ¼þ£®£¨×¢ÒâÓë0µÄÇø±ð£© ¢Ûµ¥Î»ÏòÁ¿£ºÄ£Îª1¸öµ¥Î»³¤¶ÈµÄÏòÁ¿ ÏòÁ¿a0Ϊµ¥Î»ÏòÁ¿?£üa0£ü£½1??

¢ÜƽÐÐÏòÁ¿£¨¹²ÏßÏòÁ¿£©£º·½ÏòÏàͬ»òÏà·´µÄ·ÇÁãÏòÁ¿ÈÎÒâÒ»×鯽ÐÐÏòÁ¿¶¼¿ÉÒÔÒÆµ½Í¬Ò»Ö±??ÏßÉÏ·½ÏòÏàͬ»òÏà·´µÄÏòÁ¿£¬³ÆÎªÆ½ÐÐÏòÁ¿¼Ç×÷a¡ÎbÓÉÓÚÏòÁ¿¿ÉÒÔ½øÐÐÈÎÒâµÄÆ½ÒÆ(¼´×Ô

ÓÉÏòÁ¿)£¬Æ½ÐÐÏòÁ¿×Ü¿ÉÒÔÆ½ÒƵ½Í¬Ò»Ö±ÏßÉÏ£¬¹ÊƽÐÐÏòÁ¿Ò²³ÆÎª¹²ÏßÏòÁ¿ ÊýѧÖÐÑо¿µÄÏòÁ¿ÊÇ×ÔÓÉÏòÁ¿£¬Ö»ÓдóС¡¢·½ÏòÁ½¸öÒªËØ£¬Æðµã¿ÉÒÔÈÎÒâѡȡ£¬ÏÖÔÚ±ØÐëÇø·ÖÇå³þ¹²ÏßÏòÁ¿Öеġ°¹²Ïß¡±Ó뼸ºÎÖеġ°¹²Ïß¡±¡¢µÄº¬Ò壬ҪÀí½âºÃƽÐÐÏòÁ¿Öеġ°Æ½ÐС±Ó뼸ºÎÖеġ°Æ½ÐС±ÊDz»Ò»ÑùµÄ£®

??¢ÝÏàµÈÏòÁ¿£º³¤¶ÈÏàµÈÇÒ·½ÏòÏàͬµÄÏòÁ¿ÏàµÈÏòÁ¿¾­¹ýÆ½ÒÆºó×Ü¿ÉÒÔÖØºÏ£¬¼ÇΪa?b´óСÏàµÈ£¬·½ÏòÏàͬ

?x?x2(x1,y1)?(x2,y2)??1

?y1?y22ÏòÁ¿¼Ó·¨

ÇóÁ½¸öÏòÁ¿ºÍµÄÔËËã½Ð×öÏòÁ¿µÄ¼Ó·¨ ÉèAB?a,BC?b£¬Ôòa+b=AB?BC=AC

??????£¨1£©0?a?a?0?a£»£¨2£©ÏòÁ¿¼Ó·¨Âú×ã½»»»ÂÉÓë½áºÏÂÉ£»

ÏòÁ¿¼Ó·¨ÓС°Èý½ÇÐη¨Ôò¡±Ó롰ƽÐÐËıßÐη¨Ôò¡±£º

£¨1£©ÓÃÆ½ÐÐËıßÐη¨Ôòʱ£¬Á½¸öÒÑÖªÏòÁ¿ÊÇÒª¹²Ê¼µãµÄ£¬ºÍÏòÁ¿ÊÇʼµãÓëÒÑÖªÏòÁ¿µÄʼµãÖØºÏµÄÄÇÌõ¶Ô½ÇÏߣ¬¶ø²îÏòÁ¿ÊÇÁíÒ»Ìõ¶Ô½ÇÏߣ¬·½ÏòÊÇ´Ó¼õÏòÁ¿Ö¸Ïò±»¼õÏòÁ¿ £¨2£© Èý½ÇÐη¨ÔòµÄÌØµãÊÇ¡°Ê×βÏà½Ó¡±£¬ÓɵÚÒ»¸öÏòÁ¿µÄÆðµãÖ¸Ïò×îºóÒ»¸öÏòÁ¿µÄÖÕµãµÄÓÐÏòÏ߶ξͱíʾÕâЩÏòÁ¿µÄºÍ£»²îÏòÁ¿ÊÇ´Ó¼õÏòÁ¿µÄÖÕµãÖ¸Ïò±»¼õÏòÁ¿µÄÖÕµã

µ±Á½¸öÏòÁ¿µÄÆðµã¹«¹²Ê±£¬ÓÃÆ½ÐÐËıßÐη¨Ôò£»µ±Á½ÏòÁ¿ÊÇÊ×βÁ¬½Óʱ£¬ÓÃÈý½ÇÐη¨

Ôò£®ÏòÁ¿¼Ó·¨µÄÈý½ÇÐη¨Ôò¿ÉÍÆ¹ãÖÁ¶à¸öÏòÁ¿Ïà¼Ó£º

AB?BC?CD??PQ?QR?AR£¬µ«Õâʱ±ØÐë¡°Ê×βÏàÁ¬¡±£®

3ÏòÁ¿µÄ¼õ·¨

?? ¢Ù Ïà·´ÏòÁ¿£ºÓëa³¤¶ÈÏàµÈ¡¢·½ÏòÏà·´µÄÏòÁ¿£¬½Ð×öaµÄÏà·´ÏòÁ¿ ?¼Ç×÷?a,ÁãÏòÁ¿µÄÏà·´ÏòÁ¿ÈÔÊÇÁãÏòÁ¿ ???????¹ØÓÚÏà·´ÏòÁ¿ÓУº £¨i£©?(?a)=a£» (ii) a+(?a)=(?a)+a=0£» ?????????(iii)Èôa¡¢bÊÇ»¥ÎªÏà·´ÏòÁ¿£¬Ôòa=?b,b=?a,a+b=0

????¢ÚÏòÁ¿¼õ·¨£ºÏòÁ¿a¼ÓÉÏbµÄÏà·´ÏòÁ¿½Ð×öaÓëbµÄ²î£¬ ????¼Ç×÷£ºa?b?a?(?b)ÇóÁ½¸öÏòÁ¿²îµÄÔËË㣬½Ð×öÏòÁ¿µÄ¼õ·¨ ??????¢Û×÷ͼ·¨£ºa?b¿ÉÒÔ±íʾΪ´ÓbµÄÖÕµãÖ¸ÏòaµÄÖÕµãµÄÏòÁ¿£¨a¡¢bÓй²Í¬Æðµã£© 4ʵÊýÓëÏòÁ¿µÄ»ý£º

??¢ÙʵÊý¦ËÓëÏòÁ¿aµÄ»ýÊÇÒ»¸öÏòÁ¿£¬¼Ç×÷¦Ëa£¬ËüµÄ³¤¶ÈÓë·½Ïò¹æ¶¨ÈçÏ£º

£¨¢ñ£©?a???a£»

£¨¢ò£©µ±??0ʱ£¬¦ËaµÄ·½ÏòÓëaµÄ·½ÏòÏàͬ£»µ±??0ʱ£¬¦ËaµÄ·½ÏòÓëaµÄ·½ÏòÏà

????????·´£»µ±??0ʱ£¬?a?0£¬·½ÏòÊÇÈÎÒâµÄ

¢ÚÊý³ËÏòÁ¿Âú×ã½»»»ÂÉ¡¢½áºÏÂÉÓë·ÖÅäÂÉ 5Á½¸öÏòÁ¿¹²Ïß¶¨Àí£º

????ÏòÁ¿bÓë·ÇÁãÏòÁ¿a¹²Ïß?ÓÐÇÒÖ»ÓÐÒ»¸öʵÊý?£¬Ê¹µÃb=?a

6Æ½ÃæÏòÁ¿µÄ»ù±¾¶¨Àí£º

Èç¹ûe1,e2ÊÇÒ»¸öÆ½ÃæÄÚµÄÁ½¸ö²»¹²ÏßÏòÁ¿£¬ÄÇô¶ÔÕâÒ»Æ½ÃæÄÚµÄÈÎÒ»ÏòÁ¿a£¬ÓÐÇÒÖ»ÓÐÒ»¶ÔʵÊý?1,?2ʹ£ºa??1e1??2e2£¬ÆäÖв»¹²ÏßµÄÏòÁ¿e1,e2½Ð×ö±íʾÕâÒ»Æ½ÃæÄÚËùÓÐÏòÁ¿µÄÒ»×é»ùµ× 7 ÌØ±ð×¢Òâ:

£¨1£©ÏòÁ¿µÄ¼Ó·¨Óë¼õ·¨ÊÇ»¥ÄæÔËËã £¨2£©ÏàµÈÏòÁ¿ÓëÆ½ÐÐÏòÁ¿ÓÐÇø±ð£¬ÏòÁ¿Æ½ÐÐÊÇÏòÁ¿ÏàµÈµÄ±ØÒªÌõ¼þ £¨3£©ÏòÁ¿Æ½ÐÐÓëÖ±Ï߯½ÐÐÓÐÇø±ð£¬Ö±Ï߯½Ðв»°üÀ¨¹²Ïߣ¨¼´Öغϣ©£¬¶øÏòÁ¿Æ½ÐÐÔò°üÀ¨¹²Ïߣ¨Öغϣ©µÄÇé¿ö £¨4£©ÏòÁ¿µÄ×ø±êÓë±íʾ¸ÃÏòÁ¿µÄÓÐÏòÏßÌõµÄʼµã¡¢ÖÕµãµÄ¾ßÌåλÖÃÎ޹أ¬Ö»ÓëÆäÏà¶ÔλÖÃÓÐ¹Ø Ñ§Ï°±¾ÕÂÖ÷ÒªÊ÷Á¢ÊýÐÎת»¯ºÍ½áºÏµÄ¹Ûµã£¬ÒÔÊý´úÐΣ¬ÒÔÐιÛÊý£¬ÓôúÊýµÄÔËËã´¦Àí¼¸ºÎÎÊÌâ£¬ÌØ±ðÊÇ´¦ÀíÏòÁ¿µÄÏà¹ØÎ»ÖùØÏµ£¬ÕýÈ·ÔËÓù²ÏßÏòÁ¿ºÍÆ½ÃæÏòÁ¿µÄ»ù±¾¶¨Àí£¬¼ÆËãÏòÁ¿µÄÄ£¡¢Á½µãµÄ¾àÀë¡¢ÏòÁ¿µÄ¼Ð½Ç£¬ÅжÏÁ½ÏòÁ¿ÊÇ·ñ´¹Ö±µÈÓÉÓÚÏòÁ¿ÊÇÒ»ÐµĹ¤¾ß£¬ËüÍùÍù»áÓëÈý½Çº¯Êý¡¢ÊýÁС¢²»µÈʽ¡¢½â¼¸µÈ½áºÏÆðÀ´½øÐÐ×ۺϿ¼²é£¬ÊÇ֪ʶµÄ½»»ãµã

????????

Àý1 ¸ø³öÏÂÁÐÃüÌ⣺ ¢Ù Èô|a|£½|b|£¬Ôòa=b£»

¢Ú ÈôA£¬B£¬C£¬DÊDz»¹²ÏßµÄËĵ㣬ÔòAB?DCÊÇËıßÐÎABCDΪƽÐÐËıßÐεijäÒªÌõ¼þ£»

¢Û Èôa=b£¬b=c£¬Ôòa=c£¬

¢Üa=bµÄ³äÒªÌõ¼þÊÇ|a|=|b|ÇÒa//b£» ¢Ý Èôa//b£¬b//c£¬Ôòa//c£¬

ÆäÖÐÕýÈ·µÄÐòºÅÊÇ Àý2 ÉèA¡¢B¡¢C¡¢D¡¢OÊÇÆ½ÃæÉϵÄÈÎÒâÎåµã£¬ÊÔ»¯¼ò£º

¢ÙAB?BC?CD£¬¢ÚDB?AC?BD ¢Û?OA?OC?OB?CO

Àý3Éè·ÇÁãÏòÁ¿a¡¢b²»¹²Ïߣ¬c=ka+b£¬d=a+kb (k?R)£¬Èôc¡Îd£¬ÊÔÇók

¶þ.Æ½ÃæÏòÁ¿µÄ×ø±ê±íʾ

1Æ½ÃæÏòÁ¿µÄ×ø±ê±íʾ£ºÔÚÖ±½Ç×ø±êϵÖУ¬·Ö±ðÈ¡ÓëxÖá¡¢yÖá·½ÏòÏàͬµÄÁ½¸öµ¥Î»ÏòÁ¿i,j×÷Ϊ»ùµ×ÓÉÆ½ÃæÏòÁ¿µÄ»ù±¾¶¨ÀíÖª£¬¸ÃÆ½ÃæÄÚµÄÈÎÒ»ÏòÁ¿a¿É±íʾ³Éa?xi?yj£¬ÓÉÓÚaÓë

Êý¶Ô(x,y)ÊÇÒ»Ò»¶ÔÓ¦µÄ£¬Òò´Ë°Ñ(x,y)½Ð×öÏòÁ¿aµÄ×ø±ê£¬¼Ç×÷a=(x,y)£¬ÆäÖÐx½Ð×÷aÔÚxÖáÉϵÄ×ø±ê£¬y½Ð×öÔÚyÖáÉϵÄ×ø±ê (1)ÏàµÈµÄÏòÁ¿×ø±êÏàͬ£¬×ø±êÏàͬµÄÏòÁ¿ÊÇÏàµÈµÄÏòÁ¿ (2)ÏòÁ¿µÄ×ø±êÓë±íʾ¸ÃÏòÁ¿µÄÓÐÏòÏ߶εÄʼµã¡¢ÖÕµãµÄ¾ßÌåλÖÃÎ޹أ¬Ö»ÓëÆäÏà¶ÔλÖÃÓÐ¹Ø 2Æ½ÃæÏòÁ¿µÄ×ø±êÔËË㣺

(1) Èôa??x1,y1?,b??x2,y2?£¬Ôòa?b??x1?x2,y1?y2? (2) ÈôA?x1,y1?,B?x2,y2?£¬ÔòAB??x2?x1,y2?y1? (3) Èôa=(x,y)£¬Ôò?a=(?x,

?y)

(4) Èôa??x1,y1?,b??x2,y2?£¬Ôòa//b?x1y2?x2y1?0 (5) Èôa??x1,y1?,b??x2,y2?£¬Ôòa?b?x1?x2?y1?y2

Èôa?b£¬Ôòx1?x2?y1?y2?0

3ÏòÁ¿µÄÔËËãÏòÁ¿µÄ¼Ó¼õ·¨£¬ÊýÓëÏòÁ¿µÄ³Ë»ý£¬ÏòÁ¿µÄÊýÁ¿£¨ÄÚ»ý£©¼°Æä¸÷ÔËËãµÄ×ø±ê±íʾºÍÐÔÖÊ

ÔËËãÀàÐÍ Ïò Á¿ µÄ ¼Ó ·¨ Ïò Á¿ µÄ ¼õ ·¨ Ïò Á¿ µÄ ³Ë ·¨ ¼¸ºÎ·½·¨ ×ø±ê·½·¨ ÔËËãÐÔÖÊ 1ƽÐÐËıßÐη¨Ôò 2Èý½ÇÐη¨Ôò ????a?b?(x1?x2,y1?y2) a?b?b?a ??????(a?b)?c?a?(b?c) AB?BC?AC Èý½ÇÐη¨Ôò ????a?b?(x1?x2,y1?y2) a?b?a?(?b) AB??BA OB?OA?AB ?aÊÇÒ»¸öÏòÁ¿, Âú×ã: ???>0ʱ,?aÓëaͬÏò; ???<0ʱ,?aÓëaÒìÏò; ??a?(?x,?y) ?(?a)?(??)a ???(???)a??a??a ?????(a?b)??a??b ?????=0ʱ, ?a=0 ????a¡Îb?a??b Ïò Á¿ µÄ Êý Á¿ »ý ??a?bÊÇÒ»¸öÊý a?b?x1x2?y1y2 ????a?b?b?a ??????(?a)?b?a?(?b)??(a?b) ???????(a?b)?c?a?c?b?c ????a?0»òb?0ʱ, ??a?b=0 ????a?0ÇÒb?0ʱ, ??????a?b?|a||b|cos?a,b? ???a2?|a|2,|a|?x2?y2 ????|a?b|?|a||b| Àý1 ÒÑÖªÏòÁ¿a?(1,2),b?(x,1),u?a?2b£¬v?2a?b£¬ÇÒu//v£¬ÇóʵÊýxµÄÖµ

ËÑË÷¸ü¶à¹ØÓÚ£º Æ½ÃæÏòÁ¿ÖªÊ¶µã×Ü½á µÄÎĵµ
  • ÊÕ²Ø
  • Î¥¹æ¾Ù±¨
  • °æÈ¨ÈÏÁì
ÏÂÔØÎĵµ10.00 Ôª ¼ÓÈëVIPÃâ·ÑÏÂÔØ
ÍÆ¼öÏÂÔØ
±¾ÎÄ×÷Õߣº...

¹²·ÖÏí92ƪÏà¹ØÎĵµ

Îĵµ¼ò½é£º

¸ßÖÐÊýѧ±ØÐÞ4 Æ½ÃæÏòÁ¿ ֪ʶµã¹éÄÉ Ò».ÏòÁ¿µÄ»ù±¾¸ÅÄîÓë»ù±¾ÔËËã 1ÏòÁ¿µÄ¸ÅÄ ???¢ÙÏòÁ¿£º¼ÈÓдóСÓÖÓз½ÏòµÄÁ¿ÏòÁ¿Ò»°ãÓÃa,b,c¡­¡­À´±íʾ£¬»òÓÃÓÐÏòÏß¶ÎµÄÆðµãÓëÖÕµãµÄ´óд×Öĸ±íʾ£¬È磺AB¼¸ºÎ±íʾ·¨ AB£¬a£»×ø±ê±íʾ·¨a?xi?yj?(x,y) Ïò??Á¿µÄ´óС¼´ÏòÁ¿µÄÄ££¨³¤¶È£©£¬¼Ç×÷|AB|¼´ÏòÁ¿µÄ´óС£¬¼Ç×÷£üa£ü ?ÏòÁ¿²»ÄܱȽϴóС£¬µ«ÏòÁ¿µÄÄ£¿ÉÒԱȽϴóС£® ????0ÓëÈÎÒâÏòÁ¿Æ½ÐÐÁãÏòÁ¿a£½0?£ü¢ÚÁãÏòÁ¿£º³¤¶ÈΪ0µÄÏòÁ¿£¬¼ÇΪ0£¬Æä·½ÏòÊÇÈÎÒâµÄ£¬?a£ü£½0 ÓÉÓÚ0µÄ·½ÏòÊÇÈÎÒâµÄ£¬Çҹ涨0ƽÐÐÓÚÈκÎÏòÁ¿£¬¹ÊÔÚÓйØÏòÁ¿Æ½ÐУ¨¹²Ïߣ©µÄÎÊÌâÖÐÎñ±Ø¿´Çå³þÊÇ·ñÓС°·ÇÁãÏòÁ¿¡±Õâ¸öÌõ¼þ£®£¨×¢ÒâÓë0µÄÇø±ð£© ¢Ûµ¥Î»ÏòÁ¿£º

¡Á ÓοͿì½ÝÏÂÔØÍ¨µÀ£¨ÏÂÔØºó¿ÉÒÔ×ÔÓɸ´ÖƺÍÅŰ棩
µ¥Æª¸¶·ÑÏÂÔØ
ÏÞÊ±ÌØ¼Û£º10 Ôª/·Ý Ô­¼Û:20Ôª
VIP°üÔÂÏÂÔØ
ÌØ¼Û£º29 Ôª/Ô ԭ¼Û:99Ôª
µÍÖÁ 0.3 Ôª/·Ý ÿÔÂÏÂÔØ150·Ý
ȫվÄÚÈÝÃâ·Ñ×ÔÓɸ´ÖÆ
VIP°üÔÂÏÂÔØ
ÌØ¼Û£º29 Ôª/Ô ԭ¼Û:99Ôª
µÍÖÁ 0.3 Ôª/·Ý ÿÔÂÏÂÔØ150·Ý
ȫվÄÚÈÝÃâ·Ñ×ÔÓɸ´ÖÆ
×¢£ºÏÂÔØÎĵµÓпÉÄÜ¡°Ö»ÓÐĿ¼»òÕßÄÚÈݲ»È«¡±µÈÇé¿ö£¬ÇëÏÂÔØÖ®Ç°×¢Òâ±æ±ð£¬Èç¹ûÄúÒѸ¶·ÑÇÒÎÞ·¨ÏÂÔØ»òÄÚÈÝÓÐÎÊÌ⣬ÇëÁªÏµÎÒÃÇЭÖúÄã´¦Àí¡£
΢ÐÅ£ºfanwen365 QQ£º370150219
Copyright © ÔÆÌ⺣ All Rights Reserved. ËÕICP±¸16052595ºÅ-3 ÍøÕ¾µØÍ¼ ¿Í·þQQ£º370150219 ÓÊÏ䣺370150219@qq.com