2010-2011½âÎö¼¸ºÎ ÏÂÔØ±¾ÎÄ

2010¡ª2011ѧÄêµÚһѧÆÚÆÚÄ©¿¼ÊÔ¡¶½âÎö¼¸ºÎ¡·ÊÔ¾í(A)

Ò» Ìî¿ÕÌ⣨ÿ¿Õ2·Ö£¬¹²20·Ö£©

rr1¡¢ÒÑÖªÏòÁ¿a,brµÄ·½ÏòÓàÏÒ·Ö±ðÊÇcos?1,cos?1,cos?1ºÍcos?2,cos?2,cos?2£¬ÔòÏòÁ¿aÓë

rbµÄ¼Ð½ÇÓàÏÒ=_____________________________.

rrrr?????????2¡¢Èôa?b?c?0£¬ÇÒ|a|?5,|b|?2,|c|?3£¬Ôòa?b?b?c?c?a?

rra3¡¢Èô,b????|a?b|?|a?b|³ÉÁ¢µÄ³äÒªÌõ¼þÊÇ ÊÇ·ÇÁãÏòÁ¿£¬Ôò

.

4¡¢ÖÐÐÄΪ£¨£²£¬£­£±£¬£³£©£¬°ë¾¶Îª£òµÄÇòÃæµÄ²ÎÊý·½³ÌΪ____________________________. 5¡¢µã£¨£±£¬£³£¬£°£©µ½Æ½Ãæx?2y?2z?4?0µÄÀë²îÊÇ £®

6¡¢×ÔÔ­µãÖ¸ÏòÆ½Ãæ3x?2y?6z?35?0?0nµÄµ¥Î»·¨ÏòÁ¿= .

7¡¢Ö±Ïß

x?2y?3z?1??ÓëÈý×ø±êÖáµÄ·½Ïò½Ç·Ö±ðΪ__________________. 1?12x?x0y?y0z?z0??(i?1,2)È·¶¨µÄÆ½Ãæ·½³ÌΪ______________. XiYiZi8¡¢Á½ÏֱཻÏß

9¡¢¶þ´ÎÇúÏßÖÁ¶àÓÐ________¸ö½¥½ü·½Ïò. 10¡¢ÒÑÖª¶þ´ÎÇúÏßxÐÄÇúÏß.

¶þ µ¥ÏîÑ¡ÔñÌâ(ÿÌâ2·Ö,¹²10·Ö)

2?4xy?ay2?5x?by?3?0£¬ÓÉa,bµÄÖµÅж¨,µ±__________ʱÇúÏßΪÖÐ

1¡¢ ÒÑÖªAB?c,AC?bÇÒµãD·ÖÓÐÏòÏß¶ÎBCΪm:n£¬ÔòAD?( )

A.

mc?nbmb?ncm(b?c)n(b?c) B. C. D.

m?nm?nm?nm?n22¡¢ÔÚ¿Õ¼äÖ±½Ç×ø±êϵÏ£¬·½³Ìx?y2?2xy±íʾ( )

µÚ 1 Ò³ ¹² 5 Ò³

A.Ô² B. Ë«ÇúÏß C. Á½¸ö²»Í¬µÄÆ½Ãæ D. Á½¸öÖØºÏµÄÆ½Ãæ 3¡¢ÒÑÖªÆ½Ãæ?ô£¨ £©

A£®µãA¡¢CÔÚÆ½ÃæµÄͬ²à£¬D¡¢EÔÚÁíÒ»²àÇÒBÔÚÆ½ÃæÉÏ£» B£®µãA¡¢C¡¢DÔÚÆ½ÃæµÄͬ²à£¬B¡¢EÔÚÁíÒ»²à£» C£®µãA¡¢CÔÚÆ½ÃæµÄͬ²à£¬B¡¢D¡¢EÔÚÁíÒ»²à£» D£®ÒÔÉϴ𰸶¼²»¶Ô.

:4x?5y?2z?8¼°µãA(1,1,1),B(1,0,2),C(0,0,3),D(1,?2,2)ºÍE(2,0,1),ÄÇ

?x2?y2?z2?164¡¢ÒÔÔ²?Ϊ׼ÏßµÄÔ²ÖùÃæµÄĸÏ߯½ÐÐÓÚÖ±Ïߣ¨ £©

?x?y?z?1xyzxyz??£» B£®??£» 1011?11xyzxyzC£®??£» D£®??.

?1100?11?x?a(u?v)?5¡¢ÇúÃæµÄ²ÎÊý·½³ÌΪ?y?b(u?v)(u,vΪ²ÎÊý£©£¬ÔòÇúÃæÊÇ .

?z?uv?A£®

A. µ¥Ò¶Ë«ÇúÃæ B. ˫Ҷ˫ÇúÃæ C. ÍÖÔ²Å×ÎïÃæ D. Ë«ÇúÅ×ÎïÃæ Èý ¼ÆËãÌâ(ÿÌâ10·Ö,¹²40·Ö)

rrrururrura?{1,0,0},b?{0,1,?2},c={2,?2,1}£¬ÇóÒ»µ¥Î»ÏòÁ¿m£¬Ê¹µÃm?c£¬ÇÒmÓë

1¡¢ÒÑÖªrra,b¹²Ãæ.

2¡¢ÉèÒ»Æ½ÃæÓëÒÑÖªÆ½Ãæx?2y?3z?3?0ƽÐУ¬ÇÒÓëÈý¸ö×ø±êÆ½ÃæÎ§³ÉµÄËÄÃæÌåµÄÌå»ýΪ6£¬ÊÔÇó¸ÃÆ½ÃæµÄ·½³Ì. 3¡¢ÇóÖ±Ïß·½³ÌL1?x?3?2y ÓëL2:??z?1?x?1?zµÄ¹«´¹Ïß·½³Ì. :??y?24¡¢ÒÑÖªÔ²ÖùÃæµÄ×¼ÏßÊǹýµãÇó¸ÃÔ²ÖùÃæµÄ·½³Ì. ËÄ ×ÛºÏÌâ(15·Ö)

A(1,0,0),B(0,1,0),C(0,0,1)µÄÔ²£¬Ä¸Ïß´¹Ö±ÓÚÕâÈýµãËùÔ򵀮½Ã棬

µÚ 2 Ò³ ¹² 5 Ò³

x2z22?y??1£¬ÑéÖ¤µãM(2,1,3)ÔÚÇúÃæÉÏ£¬²¢Çó¾­¹ýËüµÄÁ½ÌõֱĸÏß¡£ ÒÑÖªµ¥Ò¶Ë«ÇúÃæ49Îå Ö¤Ã÷Ìâ(µÚÒ»Ìâ7·Ö£¬µÚ¶þÌâ8·Ö£¬¹²15·Ö)

1¡¢ÉèµãOÊDz»¹²ÏßÈýµã

A,B,CËùÈ·¶¨µÄÆ½ÃæÍâÒ»µã£¬Ö¤Ã÷ËĵãA,B,C,D¹²ÃæµÄ³äÒªÌõ¼þÊÇ

OD??OA??OB??OC£¨ÆäÖÐ??????1£©.

x2y2z22¡¢ÓÉÍÖÇòÃæ2?2?2?1µÄÖÐÐÄ£¨¼´Ô­µã£©£¬ÒýÈýÌõÁ½Á½Ï໥´¹Ö±µÄÉäÏߣ¬·Ö±ð½»ÇúÃæÓÚµã

abcP1,P2,P3£¬ÉèOP1?r1,OP2?r2,OP3?r3£¬ÊÔÖ¤£º

111111?????r12r22r32a2b2c2.

2010¡ª2011ѧÄêµÚһѧÆÚÆÚÄ©¿¼ÊÔ¡¶½âÎö¼¸ºÎ¡·ÊÔ¾í(B)

Ò» Ìî¿ÕÌ⣨ÿ¿Õ2·Ö£¬¹²20·Ö£©

rrrr??????a?b?c?01¡¢Èô£¬ÇÒ|a|?5,|b|?2,|c|?3£¬Ôò(a?b)?c?_________.

rr2¡¢Èôa,b????ÊÇ·ÇÁãÏòÁ¿£¬Ôò|a?b|?|a?b|³ÉÁ¢µÄ³äÒªÌõ¼þÊÇ .

3¡¢ÖÐÐÄΪ£¨0£¬0£¬0£©£¬°ë¾¶Îª£òµÄÇòÃæµÄ²ÎÊý·½³ÌΪ____________________________. 4¡¢µã£¨£±£¬2£¬-3£©µ½Æ½Ãæ5x?3y?z?4?0µÄÀë²îÊÇ £®

5¡¢Æ½Ãæ

xyz???1(abc?0)ÓëÈý×ø±êÃæËùΧ³ÉµÄËÄÃæÌåÌå»ýÊÇ______________. abc6¡¢ÒÑÖªÈý½ÇÐÎÈý¶¥µãΪA(1,2,3),B(3,2,1),C(2,5,8)Ôò?ABCµÄÃæ»ýÊÇ .

7. Èç¹ûµã

P(2,?1,?1)¹ØÓÚÆ½Ãæ

?µÄ¶Ô³ÆµãΪ

P?(?2,3,11)£¬ÄÇô

?µÄ·½³Ì

ÊÇ .

µÚ 3 Ò³ ¹² 5 Ò³

8¡¢Á½Æ½ÐÐÖ±Ïß

x?xiy?yiz?zi??(i?1,2)È·¶¨µÄÆ½Ãæ·½³ÌΪ______________. XYZ9¡¢¶þ´ÎÇúÏßF(x,y)?0ÔÚÕý³£µã(x0,y0)´¦µÄÇÐÏß·½³ÌΪ________.

?4xy?ay2?5x?by?3?0£¬ÓÉa,bµÄÖµÅж¨,µ±__________ʱÇúÏßΪÎÞ

10¡¢ÒÑÖª¶þ´ÎÇúÏßxÐÄÇúÏß.

2¶þ µ¥ÏîÑ¡ÔñÌâ(ÿÌâ2·Ö,¹²10·Ö)

1¡¢ ÒÑÖªAB?c,AC?bÇÒµãD·ÖÓÐÏòÏß¶ÎBCΪn:m£¬ÔòAD?( )

A.

mc?nbmb?ncm(b?c)n(b?c) B. C. D.

m?nm?nm?nm?n22¡¢ ÔÚÆ½ÃæÖ±½Ç×ø±êϵÏ£¬·½³Ìx?y2?2xy±íʾ( )

A.Ô² B. Ë«ÇúÏß C. Á½Ìõ²»Í¬µÄÖ±Ïß D. Á½ÌõÖØºÏµÄÖ±Ïß 3ÒÑÖªÁ½Ïà½»Æ½Ãæ£º?1:3x?y?2z?3?0Óë?2:x?2y?z?4?0ÒÔ¼°µãM(2,?1,1)ºÍ

N(1,2,?3)£¬ÔòÕâÁ½µãÔÚ£¨ £©

A£®?1Óë?2Ëù³Éͬһ¶þÃæ½ÇÄÚ£» B£®?1Óë?2Ëù³ÉµÄÏàÁÚ¶þÃæ½ÇÄÚ£» C£®?1Óë?2Ëù³ÉµÄ¶Ô¶¥¶þÃæ½ÇÄÚ£» D£®ÒÔÉϴ𰸶¼²»¶Ô.

?(x?2)2?y2?44¡¢½«Ô²?ÈÆxÖáÐýת²úÉú£¨ £©

?z?0A£®»·Ã棻 B£®»·×´ÇøÓò£» C£®ÇòÃæ£» D£®ÈÔÊÇ´ËÔ².

x2y2z2?2?2?12222a?b?c?0,k?a,k?b,ca?kb?kc?k5¡¢ÒÑÖª·½³Ì£¨ÆäÖУ©Ôòµ±kÂú

×㣨 £©Ê±£¬·½³Ì±íʾһ˫Ҷ˫ÇúÃæ. A. k?c2 B. b2?k?c2

2C. a?k?b2 D. b2?k?a2»òc2?k?b2

µÚ 4 Ò³ ¹² 5 Ò³

Èý ¼ÆËãÌâ(ÿÌâ10·Ö,¹²40·Ö)

rrrrrrrrrraÓëbµÄ¼Ð½Ç.

1¡¢ÈôÏòÁ¿a?3b´¹Ö±ÏòÁ¿7a?5b£¬ÏòÁ¿a?4b´¹Ö±ÏòÁ¿7a?2b£¬ÇóÏòÁ¿

?2x?y?z?3?0?x?y?2z?3?0£¬ÇÒÓëÆ½Ãæx?y?z?18?0´¹Ö±µÄÆ½Ãæ·½³Ì.

2¡¢Çóͨ¹ýÖ±Ïß? 3¡¢ÇóÁ½Ö±Ïߣºl1:xyzx?1y?2z?3µÄ¹«´¹Ïß·½³Ì. ??£¬l2:??125234A(1,0,0),B(0,1,0),C(0,0,1)µÄÔ²£¬ÇÒÖáÏß´¹Ö±

4¡¢ÒÑÖªÔ²×¶ÃæµÄ¶¥µãÔÚ×ø±êÔ­µãO£¬×¼ÏßÊǹýµãÓÚÕâÈýµãËùÔ򵀮½Ã棬Çó¸ÃÔ²×¶ÃæµÄ·½³Ì. ËÄ ×ÛºÏÌâ(15·Ö)

x2y2z2???1£¬ÑéÖ¤µãM(2,3,2)ÔÚÇúÃæÉÏ£¬²¢Çó¾­¹ýËüµÄÁ½ÌõֱĸÏß¡£ ÒÑÖªµ¥Ò¶Ë«ÇúÃæ494Îå Ö¤Ã÷Ìâ(µÚÒ»Ìâ7·Ö£¬µÚ¶þÌâ8·Ö£¬¹²15·Ö)

1¡¢Ö¤Ã÷ÓÉÆ½Ãæ

xyz???1ÓëÈý×ø±êÖáµÄ½»µãËù³ÉµÄÈý½ÇÐεÄÃæ»ýΪ£º abc122bc?a2c2?b2a2 22¡¢ÒÑÖªÆ½Ãæ

?:Ax?By?Cz?D?0ÓÚM£¬ÇÒM1MÒÔ¼°²»ÔÚ

?ÉϵÄÁ½µã

M1(x1,y1,z1)ºÍ

M2(x2,y2,z2)£¬Ï߶ν»???MM2£¬ÇóÖ¤:

???Ax1?By1?Cz1?D.

Ax2?By2?Cz2?D

µÚ 5 Ò³ ¹² 5 Ò³