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2022年平面向量线性运算数量及运算 .pdf

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1、PMNCABQ平面向量专题一：向量的线性运算例1（1）设ED，分别是ABC的边BCAB，上的点,ABAD21,BCBE32,若ACABDE21(21，为实数),则21的值为 _.（2）已知平行四边形ABCD，E为AD中点，点F在AB上，且3AFFB，AC与EF相交于点G，则AGAC（3）如图，设P、Q为ABC内的两点，且2155APABAC，AQ23AB14AC，则ABP的面积与ABQ的面积之比为()A15B45C14 D13（4）已知等差数列an的前n项和为Sn，若OBa1OAa200OC，且A，B，C三点共线（该直线不过原点O），则S200（）A100 B101 C200 D201（5）给

2、定两个长度为1 的平面向量OA和OB，它们的夹角为120o.如图所示，点C在以 O为圆心的圆弧AB上变动.若,OCxOAyOB其中,x yR,则xy的最大值是 _.（6）如图，平面内有三个向量OA、OB、OC,其中与 OA 与 OB 的夹角为120，OA 与 OC的夹角为30,且|OA|OB|1，|OC|32，若 OC OA+OB（，R）,则+的值为 .例 2、在 OAB中，OAOC41，OBOD21，AD与 BC交于 M点，设aOA，bOB，（1）试用a和b表示向量OM（2）在线段 AC上取一点E，线段 BD上取一点F，使 EF过 M点，设OAOE，OBOF。求证：17371例 3、（1）已

3、知a=（1，2），b=（3，2），当 ka+b与a3b平行，k 为何值（）A 14 B 14 C 31 D 31（2）已知222,cos,21sinambmm且2ab，则m的取值范围是。例 4、已知向量()()()()3,4,6,3,5,3OAOBOCmm=-=-=-+（1）若点A、B、C不能构成三角形，求实数m应满足的条件；（2）若ABCD为直角三角形，求实数m的值.专题二：平面向量与三角形“四心”问题例 5、（1）已知G是ABC所在平面上的一点，若0GAGBGC，则G是ABC的；（2）P是ABC所在平面上一点，若PAPCPCPBPBPA，则P是ABC的；（3）已知I为ABC所在平面

4、上的一点，且ABc，ACb，BCa 若0aIAbIBcIC，则I是ABC的；解：IBIAAB，ICIAAC，则由题意得()0abc IAbABcAC，ABACbABcACACABABACACABABAC，文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P

5、1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10

6、P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY1

7、0P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY

8、10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 H

9、Y10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7

10、HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7

11、 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1bcABACAIabcABACABAB与ACAC分别为AB和AC方向上的单位向量，AI与BAC平分线共线，即AI平分BAC（4）已知O是ABC所在平面上一点，若222OAOBOC，则O是ABC的；练习：（1）在同一个平面上有ABC及一点O满足关系式：2OA2BC2OB2CA2OC2AB，则O为ABC的（）外心内心C 重心D 垂心（2）已知 ABC，P 为三角形所在平面上的动点，且动点 P 满足：PAPCPAPB0PBPC，则 P 点为三角形的（）外心内心C

12、重心D 垂心(3).点O是ABC所在平面内的一点，满足OA OBOB OCOC OA，则点O是ABC的；例 6、（1）已知O是平面上一定点，ABC，是平面上不共线的三个点，动点P满足()OPOAABAC，(0)，则P的轨迹一定通过ABC的；（2）已知O是平面上一定点，ABC，是平面上不共线的三个点，动点P满足coscosABACOPOAABBACC，(0)，则动点P的轨迹一定通过ABC的；（3）已知O是平面上一定点，ABC，是平面上不共线的三个点，动点P满足ABACOPOAABAC，(0)，则动点P的轨迹一定通过AB

13、C的；（4）已知O是平面上的一定点，ABC，是平面上不共线的三个点，动点P满足2coscosOBOCABACOPABBACC，(0)，则动点P的轨迹一定通过ABC的；专题三：平面向量的数量积运算文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3

14、ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3

15、 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X

16、3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10

17、X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N1

18、0X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N

19、10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3

20、N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1例 7、（1）已知向量AB与AC的夹角为120,且3AB,2AC,若APABAC且APBC,则实数的值为 _.（2）已知ABC为等边三角形，AB=2，设点 P，Q 满足ABAP，ACAQ)1(，R，若32BQ CP，则=（A）21（B）221（C）2101（D）2223(3)在平行四边形ABCD中，3A，边AB、AD的长分别为2、1，若M、N分别是边BC、CD上的点，且满足|CDCNBCBM，则ANAM的取值范围是。(4)已知正方形ABCD 的边长为1，点 E 是 AB 边

21、上的动点，则CBDE的值为 _；DCDE的最大值为 _。【解析】设CDCNBCBM=（01），则BCBM=AD,DCDN)1(=AB)1(，则ANAM=)(DNADBMAB=)1()(ABADADAB=ADAB+2)1(AB+2AD+ABAD)1(,又ADAB=2 13cos=1，2AB=4，2AD=1，ANAM=6)1(5222，01，2ANAM5，即ANAM的取值范围是 2,5.（5）对任意两个非零的平面向量和，定义若平面向量,a b满足0ab，ab与的夹角)4,0(，且ba和ab都在集合|2Znn中，则ba=A12B.1 C.32D.52文档编码:CN4M6L3S9Y7 HY10P1N3

22、N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N

23、3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1

24、N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P

25、1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10

26、P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY1

27、0P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY

28、10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1解：因为22coscos|babbbaba，1coscos|abaaabab，且ba和ab都在集合|2Znn中，所以21c

29、os|abab，cos21|ab，所以2cos2cos|2baba，因为)4,0(，所以21ba，故有23ba故选 C(6)若平面向量,a b满足：23ab，则a b的最小值是_。例 8、在 ABC中，满足ABAC与的夹角为060，M 是 AB 的中点（1）若ABAC，求向量2ABACAB与的夹角的余弦值；（2）若2,2 3ABBC，在 AC 上确定一点D 的位置,使得DB DM达到最小，并求出最小值.例 9、（1）已知(2,0),(2,2),(2 cos,2 sin)()OBOCCAR，则OA与OB夹角的范围为（其中O为坐标原点）（）A、0,4 B、5,4 12 C、5,122 D、5,12

30、 12（2）若对一切R,cos,2sinmaa的长度不超过2，则实数a的取值范围是 _.（3）已知圆O的半径为1，PA、PB为该圆的两条切线，A、B为两切点，那么PAPB的最小值为（）(A)42 (B)32 (C)42 2 (D)322【解析1】如图所示：设PA=PB=x(0)x,APO=,则 APB=2，PO=21x，21sin1x，文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档

31、编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文

32、档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1

33、文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T

34、1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4

35、T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V

36、4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9

37、V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1|cos2PAPBPAPB=22(12sin)x=222(1)1xxx=4221xxx，令PAPBy，则4221xxyx，即42(1)0 xy xy，由2x是实数，所以2(1)41()0yy，2610yy，解得32 2y或32 2y.故min()32 2PA PB.此时21x.【解析2】设,0APB，2cos1/tancos2PA

38、PBPAPB2222221sin12sincos22212sin2sinsin22换元：2s i n,012xx，1121232 23xxPAPBxxx【解析 3】建系：园的方程为221xy，设11110(,),(,),(,0)A x yB xyP x，2211101110110,001AOPAx yxxyxx xyx x222222221100110110221232 23PA PBxx xxyxxxxx（4）设,x y zR,且满足:2221xyz,2314xyz,则xyz_.（5）已知sin2cos5则tan。22210110111001,2PA PBxxyxxyxx xxyP A B

39、 O 文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9

40、V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z

41、9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2

42、Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N

43、2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10

44、N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH1

45、0N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH

46、10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 Z

47、H10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3

48、ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3

49、 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X

50、3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10X3 ZH10N2Z9V4T1文档编码:CN4M6L3S9Y7 HY10P1N3N10

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