16£®ÒÑÖª¡÷OABµÄ¶¥µã×ø±êΪO£¨0£¬0£©£¬A£¨1£¬3£©£¬B£¨6£¬-2£©£¬ÓÖµãP£¨-2£¬1£©£¬µãQÊDZßABÉÏÒ»µã£¬ÇÒ$\overrightarrow{OQ}$•$\overrightarrow{AP}$=-10£®
£¨1£©ÇóµãQµÄ×ø±ê£»
£¨2£©ÈôRΪÏ߶ÎOQ£¨º¬¶Ëµã£©ÉϵÄÒ»¸ö¶¯µã£¬ÊÔÇó£¨$\overrightarrow{RO}$+$\overrightarrow{RP}$£©•£¨$\overrightarrow{RA}$+$\overrightarrow{RB}$£©µÄÈ¡Öµ·¶Î§£®

·ÖÎö £¨1£©ÏÈÉè$\overrightarrow{AQ}$=¦Ë$\overrightarrow{AB}$£¬¸ù¾ÝÏòÁ¿ÊýÁ¿»ý¹Øϵ$\overrightarrow{OQ}$•$\overrightarrow{AP}$=-10½â·½³ÌÇó³ö¦Ë¼´¿É£®
£¨2£©ÓÉRΪÏ߶ÎOQÉϵÄÒ»¸ö¶¯µã¿ÉÉèR£¨2t£¬2t£©£¬ÇÒ0¡Üt¡Ü1£¬·Ö±ðÇó³ö$\overrightarrow{RO}$£¬$\overrightarrow{RP}$£¬$\overrightarrow{RA}$£¬$\overrightarrow{RB}$µÄÏòÁ¿×ø±ê£¬ÓÉÏòÁ¿µÄÊýÁ¿»ý$\overrightarrow{RO}$+$\overrightarrow{RP}$£©•£¨$\overrightarrow{RA}$+$\overrightarrow{RB}$ÕûÀí¿ÉµÃ¹ØÓÚtµÄÒ»Ôª¶þ´Îº¯Êý£¬ÀûÓöþ´Îº¯ÊýµÄ֪ʶ¿ÉÇóÈ¡Öµ·¶Î§£®

½â´ð ½â£º£¨1£©$\overrightarrow{AP}$=£¨-3£¬-2£©£¬$\overrightarrow{AB}$=£¨5£¬-5£©£¬
¡ßµãQÊDZßABÉÏÒ»µã£¬
¡àÉè$\overrightarrow{AQ}$=¦Ë$\overrightarrow{AB}$=£¨5¦Ë£¬-5¦Ë£©£¬
$\overrightarrow{OQ}$=$\overrightarrow{OA}$+$\overrightarrow{AQ}$=£¨1£¬3£©+£¨5¦Ë£¬-5¦Ë£©=£¨1+5¦Ë£¬3-5¦Ë£©£¬
¡ß$\overrightarrow{OQ}$•$\overrightarrow{AP}$=-10£®
¡à-3£¨1+5¦Ë£©-2£¨3-5¦Ë£©=-10£¬
¼´¦Ë=$\frac{1}{5}$£¬Ôò$\overrightarrow{OQ}$=£¨1+5¡Á$\frac{1}{5}$£¬3-5¡Á$\frac{1}{5}$£©=£¨2£¬2£©£®
¼´Q£¨2£¬2£©£®
£¨2£©¡ßRΪÏ߶ÎOQÉϵÄÒ»¸ö¶¯µã£¬¡àÉèR£¨2t£¬2t£©£¬ÇÒ0¡Üt¡Ü1£¬
Ôò$\overrightarrow{RO}$=£¨-2t£¬-2t£©£¬$\overrightarrow{RP}$=£¨-2-2t£¬1-2t£©£¬$\overrightarrow{RA}$=£¨1-2t£¬3-2t£©£¬$\overrightarrow{RB}$=£¨6-2t£¬-2-2t£©£¬
Ôò£¨$\overrightarrow{RO}$+$\overrightarrow{RP}$£©•£¨$\overrightarrow{RA}$+$\overrightarrow{RB}$£©=£¨-2-4t£¬1-4t£©•£¨7-4t£¬1-4t£©
=£¨-2-4t£©£¨7-4t£©+£¨1-4t£©£¨1-4t£©=32t2-28t-13
=32£¨t-$\frac{7}{16}$£©2-$\frac{153}{8}$£¬
¡ß0¡Üt¡Ü1£¬
¡àµ±t=$\frac{7}{16}$ʱ£¬º¯ÊýÈ¡µÃ×îСֵ-$\frac{153}{8}$£¬
µ±t=1ʱ£¬º¯ÊýÈ¡µÃ×î´óÖµ-9£¬
¼´£¨$\overrightarrow{RO}$+$\overrightarrow{RP}$£©•£¨$\overrightarrow{RA}$+$\overrightarrow{RB}$£©µÄ·¶Î§ÊÇ[-$\frac{153}{8}$£¬-9]£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éƽÃæÏòÁ¿Ó뺯ÊýµÄ×ÛºÏÎÊÌâÖУ¬ÀûÓÃÏòÁ¿µÄÊýÁ¿»ý£¬ÏòÁ¿¹²ÏßµÄ×ø±ê¹«Ê½½øÐÐת»¯£¬×îºóת»¯Îªº¯ÊýµÄÎÊÌ⣬ÀûÓöþ´Îº¯ÊýÔÚ±ÕÇø¼äÉϵÄ×îÖµÊǽâ¾ö±¾ÌâµÄ¹Ø¼ü£®×ÛºÏÐÔ½ÏÇ¿£¬ÔËËãÁ¿½Ï´ó£¬¿¼²éѧÉúµÄ¼ÆËãÄÜÁ¦£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÔËÐÐÈçͼ³ÌÐò¿òͼ£®
£¨1£©µ±ÊäÈëxµÄÖµµÈÓÚ2¦Ðʱ£¬ÇóÊä³öyµÄÖµ£»
£¨2£©µ±Êä³öyµÄÖµ×î´óʱ£¬ÇóÊäÈëxµÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

7£®ÒÑÖª¹«²î²»Îª0µÄµÈ²îÊýÁÐ{an}Âú×㣺a1=2£¬ÇÒa1¡¢a2¡¢a5³ÉµÈ±ÈÊýÁУ¬ÔòÊýÁÐ{an}µÄͨÏʽÊÇan=4n-2£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

4£®É踴Êýz=£¨a2-1£©+£¨a-1£©i£¨iÊÇÐéÊýµ¥Î»£¬a¡ÊR£©£¬ÈôzÊÇ´¿ÐéÊý£¬ÔòʵÊýa=-1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®Èçͼ£¬ÔÚÖ±½Ç×ø±êƽÃæxOyÄÚÒÑÖª¶¨µãF£¨1£¬0£©£¬¶¯µãPÔÚyÖáÉÏÔ˶¯£¬¹ýµãP×÷PM½»xÖáÓÚµãM£¬Ê¹µÃ$\overrightarrow{PM}$•$\overrightarrow{PF}$=0£¬ÑÓ³¤MPµ½µãN£¬Ê¹µÃ|$\overrightarrow{PM}$|=|$\overrightarrow{PN}$|
£¨1£©µ±|$\overrightarrow{OP}$|=1ʱ£¬Çó$\overrightarrow{FM}$•$\overrightarrow{FN}$£»
£¨2£©ÇóµãNµÄ¹ì¼£·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

1£®ÒªÔڰ뾶OA=90cmµÄÔ²ÐÎľ°åÉϽØÈ¡Ò»¿éÉÈÐΣ¬Ê¹Æ仡$\widehat{AB}$µÄ³¤Îª30¦Ðcm£¬ÔòÔ²ÐĽǡÏAOB=$\frac{¦Ð}{3}$£¨Ì¶È£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

8£®ÉèÕý·½ÌåµÄËùÓÐÀⳤ¶¼Îªa£¬¶¥µã¶¼ÔÚÒ»¸öÇòÃæÉÏ£¬Ôò¸ÃÇòµÄ±íÃæ»ýΪ£¨¡¡¡¡£©
A£®¦Ða2B£®2¦Ða2C£®3¦Ða2D£®12¦Ða2

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®Èçͼ4£¬ÒÑÖªÕýÈýÀâÖùABC-A1B1C1£¬ÑÓ³¤BCÖÁD£¬Ê¹CΪBDµÄÖе㣮
£¨1£©ÇóÖ¤£ºÆ½ÃæAC1D¡ÍƽÃæAA1B£»
£¨2£©ÈôAC=2£¬AA1=4£¬Çó¶þÃæ½ÇC1-AD-BµÄÓàÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÒÑÖªº¯Êýf£¨x£©=£¨a+1£©lnx-ax£¬ÊÔÌÖÂÛf£¨x£©ÔÚ¶¨ÒåÓòÄڵĵ¥µ÷ÐÔ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸