www.77dmdm的相关:18学年高中数学第二章平面向量6平面向量数量积的坐标表示教学案北师大版必修4

zd1118.com www.bdg9.com hg7634com xinu566.com www.72205588.com WWW.CCC085.COM qyy1969com

www.96455.com ycqwee123 www127488com WWW.81444018.COM www.six358.com fy88tk wwwslcai88com

6 平面向量数量积的坐标表示 [核心必知] 1.向量数量积的坐标表示 设 a=(x1,y1),b=(x2,y2),则 a·b=x1x2+y1y2. 即两个向量的数量积等于相应坐标乘积的和. 2.度量公式 (1)长度公式:设 a=(x,y),则|a|= x +y . (2)夹角公式: 设 a=(x1, y1), b=(x2, y2), a 与 b 的夹角为 θ , 则 cos θ = 3.两向量垂直的坐标表示 设 a=(x1,y1),b=(x2,y2),则 2 2 x1x2+y1y2 . 2 2 x +y1 x2 2+y2 2 1 a⊥b?a·b=0?x1x2+y1y2=0. 4.直线的方向向量 给定斜率为 k 的直线 l,则向量 m=(1,k)与直线 l 共线,把与直线 l 共线的非零向量 m 称 为直线 l 的方向向量. [问题思考] 1.由向量长度的坐标表示,你能否得出平面内两点间的距离公式? 提示:设 A(x1,y1),B(x2,y2), 则 AB =(x2-x1,y2-y1),由向量长度的坐标表示可得 |AB|=| AB |= x2-x1 2 + y2-y1 2 . 2.坐标形式下两向量垂直与平行的条件有何区别? 提示:设 a=(x1,y1),b=(x2,y2),则: a⊥b?x1x2+y1y2=0,即“相应坐标相乘和为 0”; -1- a∥b?x1y2-x2y1=0,即“坐标交叉相乘差为 0”. 3.直线 l 的方向向量唯一吗? 提示:直线 l 的方向向量即是与 l 平行的向量,意指表示该向量的有向线段所在的直线与 l 平行或重合,所以直线 l 的方向向量不唯一(有无数个),但它们都是共线向量. 讲一讲 1.已知向量 a=(4,-2),b=(6,-3),求: (1)(2a-3b)·(a+2b); (2)(a+b) . [尝试解答] 法一:(1)∵2a-3b=(8,-4)-(18,-9)=(-10,5), 2 a+2b=(4,-2)+(12,-6)=(16,-8), ∴(2a-3b)·(a+2b)=-160-40=-200. (2)∵a+b=(10,-5) ∴(a+b) =(10,-5)×(10,-5)=100+25=125. 法二:由已知可得:a =20,b =45,a·b=30 (1)(2a-3b)·(a+2b)=2a +a·b-6b =2×20+30-6×45=-200. (2)(a+b) =a +2a·b+b =20+60+45=125. 2 2 2 2 2 2 2 2 进行向量的数量积的坐标运算关键是把握向量数量积的坐标表示,运算时常有两条途径: (1)根据向量数量积的坐标表示直接运算; (2)先利用数量积的运算律将原式展开,再依据已知计算. -2- 练一练 1.已知 a=(2,1),b=(-1,3),向量 c 满足 a·c=4,b·c=-9. (1)求向量 c 的坐标; (2)求(a+b)·c 的值. 解:(1)设 c=(x,y), 由? ? ?a·c=4, ? ?2x+y=4, 得,? ?b·c=-9, ?-x+3y=-9. ? ? 解得 x=3,y=-2. ∴c=(3,-2). (2)法一:∵a+b=(2,1)+(-1,3)=(1,4), ∴(a+b)·c=(1,4)·(3,-2) =1×3+4×(-2) =-5. 法二:(a+b)·c =a·c+b·c =(2,1)·(3,-2)+(-1,3)·(3,-2) =2×3+1×(-2)+(-1)×3+3×(-2) =-5. 讲一讲 2.已知 a=(1,2),b=(-2,-4),|c|= 5. (1)求|a+2b|; 5 (2)若(a+b)·c= ,求向量 a 与 c 的夹角. 2 [尝试解答] (1)a+2b=(1,2)+2(-2,-4)=(-3,-6) ∴|a+2b|= (-3) +(-6) =3 5. (2)∵b=(-2,-4)=-2(1,2)=-2a ∴a+b=-a, 5 ∴(a+b)·c=-a·c= 2 设 a 与 c 的夹角为 θ , -32 2 a·c 1 则 cos θ = = =- |a||c| 2 5× 5 2 ∵0≤θ ≤π ,∴θ = π 3 2 即 a 与 c 的夹角为 π . 3 - 5 2 1.已知向量的坐标和向量的模(长度)时,可直接运用公式|a|= x +y 进行计算. 2.求向量的夹角时通常利用数量积求解,一般步骤为: (1)先利用平面向量数量积的坐标表示求出两向量的数量积; (2)再求出两向量的模; (3)由公式 cos θ = 2 2 a·b 计算 cos θ 的值; |a||b| (4)在[0,π ]内,由 cos θ 的值确定角 θ . 练一练 2.已知向量 a=(x1,y1),b=(x2,y2),e=(0,1),若 a≠b,|a-b|=2,且 a-b 与 e 的 π 夹角为 ,则 x1-x2=( 3 A.2 C.± 2 ) B.± 3 D.±1 解析:选 B a-b=(x1-x2,y1-y2). ∴(a-b)·e=(x1-x2)×0+(y1-y2)×1=y1-y2. π ∵|a-b|=2,|e|=1,a-b 与 e 的夹角为 , 3 ∴cos π (a-b)·e y1-y2 1 = = = ,∴y1-y2=1, 3 |a-b||e| 2 2 2 2 又由|a-b|=2 知,(x1-x2) +(y1-y2) =4, ∴(x1-x2) =3.∴x1-x2=± 3. 2 讲一讲 3? ?1 3.已知 a=( 3,-1),b=? , ?. ?2 2 ? (1)求证:a⊥b; -4- (2)是否存在实数 k,使 x=a-2b,y=-ka+b,且 x⊥y,若存在,求 k 的值;不存在,请 说明理由. 1 3 [尝试解答] (1)证明:∵a·b= 3× +(-1)× =0. 2 2 ∴a⊥b. 3? ?1 (2)∵x=( 3,-1)-

以下是今天幸运会员获奖名单

ob829.com,ww90020,www.js8894.com,www.9799.com,www.112cp.com,www.qqq252.com,111tt,www.114sihu.com,ak1844,www.47769.com,sjp520,linpin66

99vv163com,www.www00996.com,789mmm,www.965989.com,wb6372com,yh7653.com,xpj2466.com,mxpj567.com,cha258.com,zuoyu530,www.88996609.com,cp0523com,www.inhao77.com,www.111zyz.com,男女生污污的视频带声音,54902g.co,000990.com,www.658223.com,jjszy2com,wwwcp08jcom,http://hy0113co,www233438com,855jj.cn,www.jb568.com,hg7003com,www.55229.com,34123com,www.dsv8j.cn,WWW.TM3939.COM,www0099crcom,xf3731516,www.89699.com,WWW.LXCCD.COM,ag3173com,17788xxoo.com,www.554532.com,www.5263.com,www07188com,www.85969.com,lh9829.com,www.00000b.com,868229.com,wwwcs896com,1038.com,WWW.75587.NET,www.av12com,www.4887.com,www.kk3.cc,cldizhi,amhg008.com,vw635.com,fenfencaocom,22588com,www9655com,www.5266758.com,www.haole018.com,ccc36dizhi@gmail.com,816452com,wwwyh4818com,7077.com,a870818a,77h.com,www.ag.dhygw775.com,wwwlxyl037com,zj3388.com,www.511ab.com,www.69sxy.com,wwwm3666com,45456575,555331.com,www.jsdc48.com,gen104,www862970com,www68856com,chaopengzaixiangongkaishipingengxin,wwwyzh222com,meil,wwwyzc523com,hbnder,www.1050.com,ag2362com,long233.com,www.drf678.com,6656k.com,WWW.881398.COM,www.915298.com,831241com,64144.com,www.0909qq.com,xxssw1232,www.9999c9.com,70988.com,mg8535.vip,www.bg725.com,shoushoumenshipin,ctt820.cc,wwwswty0777com,www2648icom,www.177234.com,0055365.com,www.pixiu173.com,ccc464.com,www69388net,mg8347.vip,hzh045,wwwbm3223com,www.3766.cn,zhujiayuan,www9927oocom,www.12.cc,wy1980,Lsn zxzy,ag89725,wwwsanya4444com,9999134.com,wwwxpj81238com,154984727,811503500,32626.com,www.69sxy.com,ks015.com,WWW.9365.TW,l62226.com,www.852666.com,hg1061.net,35345.com,xkxkxk,11000com,www.gz2288.com,th3333.com,mg507.com,d5544com,xeq123,www.bm1050.com,www.ccc223.com,225577com,hg0399.com,www.j8av.com,WWW.CG998.NET,10050758.com,77k.0033,k9bbb.com,www.699857.com,www.13010.com,03xpjcom,ag9241vip,6155.com,qy7794vip,www.1355355.com,www1690kkcom,miyanan,libby3313@163.com,wwwampj68696com,www63700com,www.65**b.com,wwwpj99ocom,835xy在线视频,www.3995522.com,zunyi254.com,jingyingyulecheng,613678.com,www.k8068.com,803343com,wwwhg2557com,www.tutunew.con,xie209,www.wzh133585.com,www588778com|

www.m.772089.com,www30555xpjcom,www.46686.net,www.longdu707.com,www.95443.wn88888.com,www.672811.com,www.ssc905.com,www.h538.com,bbs.111555.com,5360rr,www.9088222.com,mh5577.com,aomenwangshangyulezhucesong1yuancaijin,d y 1177,大片网,bet750.com,c442886842,www.990033.com,www.se192z.com,wwwbole567com,m.ks8777.com,shan0701,fc5789.com,www.9758.con,yh7192.com,www.995998.com,www.vns13177.com,wwwbjn2com,93797com,360189z,22333av,jinsonglu,www.wdz1.com,138tkcom,aa1689,1633.co,www.733888.com,WWW.09500.COM,jb807com,rb0454com,867675com,wwww.hs653c0m,aa126,ask5555.com,wwwhg6261com,xiaowei388.com,wwwbvip92com,99tv. con,www.63416.com,www.haogod.com,qingdaotianqiyubao,2390lb.com,sifangbobochengrenshequ,jp5555.com,73037,7616n,qinlong520,6699bw.com,www.mszq.com,www930900com,www.win789.com,66657.com,www.93334.com,ks0990.com,www.1588.com,www.hg83332.com,wwwhp77777com,www0011mmmmcom,cheng5566,www.336296.com,www38989xcom,c73116com,az1114az,121121,www.6020011.com,www.53368.com,wwwii269com,wwwy54ccom,www0137com,491616.com,9947756,78848、com,44pp.net,www.7607633.com,www.g0124.com,YeYeMo,aaa7977,wwwg8838com,www533345com,www.996654.com,549856987,911zy.cc,ag8394com,www510amcom,www.lhc111.com,www789255com,www.5k6b.com,wwwspj22com,asdse,www.110408.com,www32424com,zhuweizhong,uanjiwang.com,ca991639562,m.ks2888.com,www.dhy.cc,www.hg673.com,www.9912df.com,www9997tw,www.g22331.com,95990222net,www.sasa66.com,www.108msc.com,3556ylccom,655985.com,js4272com,www.777aj.com,55kk44wwcom,plws999.com,www.22dxdx.com,www.myavok.com,js0627com,wwwg1080com,b13925699003,shujin,vns0937com,wwwbetvip-9com,ag1297vip,sky321,3762vip,www.14dgbyg.con,caonimaya1,qiuqq,hg1118.com,97zaixianxianmianfeiguankanshipinzaixianguankan,8331yy.com,www8899net,www.4577j.com,pj795.com,www.hg2097.com,www.qinglouav.com,www.367cf,46467946,www.61511.com,zsyozjyy,www.549345.com,WWW.222993.COM,lhc677小马哥,00899t,www0033ggcom,www.632345.com,www.00880002.com,www.53638.com,www.9797e.com,wap.sogou.com/web/id,wwwgz-haibangcom,www.1592k.com,lehu3221com,www.hg356.com,yaya1986,1225684309@qq.com,www.stt,口袋影院,wwwapplecomcn,bw3388guojiyule,wwwhg93678com,www.9170166.com,www.ccc007.com|

wwwsands145com,www.hf529.com,WWW.A56789.COM,www.yehualu.com,lehu416,www.ykfwbj.com,www.bmw0033.com,hg64.com,zhang1991,wwwbm3196com,hg8585f.com,www.55663885.com,yabo7118.com,ks558.vip,www.sun846.com,www.29066.com,lilai9898.com,a13272475337,www.159444.com,www.w9437.com,www7378ccom,kj657com,www.sun95888.com,www.208017.com,wwwam2588com,www.444480.com,js96008,yobetyobet753.com,www.7868e.com,15611604618,www3458ppcom,am3988.com,www.6660.com,www.cn3369.com,wwwjsc33com,kwyi4. xyz,www.nydh.xyz,wwwwan0008com,www.25ah.com,www.63549.com,wwwp5555ecom,hhjt9999.com,www.nwmpb.com,wwwxpj9332com,偷拍亚洲色自拍,73aaa.com,www.365all.com,www.a8002.com,015488.com,6164com,www.bm6249.com,www.777ex.com,ifang123,20174222com,www.y03.com,www.qp0044.com,www.8807178.com,www.myuanlin.com,WWW.10533.COM,www.9676911.com,www.8866666.com,amvip309,www.172244.com,296543.com,www.3550q.com,tlh11,908321.com,aa8299,317562754@qq.com,c1397199880,yb0592com,www.v9026.com,00899s,www.sk4383.com,wenjincheng,www.hg7330.com,nibaofa..com,wan6778.com,www.pu130.com,wwwjd998.com,9696yhcom,2061322,www8850060com,www2260ncom,www.910tt,www.bet4232.com,9777.win,bengtuan4439,www.51425.com,kkkwww679,www.mw183.com,www.885683.com,WWW.6896.COM,pb0222.com,WWW.FC448.COM,www.x8882.com,447270719@qq.com,wwwcp6pw,www.888coown.com,www.x5999.com,334168531@qq.com,68890,777888kg.com,8804rr,www.72544.com,qqzwj520,baojianyoushengxiaoshuo,a2971118,851916com,77729.com,www.8802jj.com,wangshangbaijialeduida,www.208sihu,com,wsz13633,www3337msccom,yuanyexiaonian,ag0663cn,hj89akj,www631155com,www.ye321.cn,882650com,www.266751.com,www.1114698.com,www.tyfo.com,www44166com,www.5000016.com,www.hshg22.com,60336.com,www.2255760.com,www.bm66666.com,www402365com,www067876com,Por*hu*,1c11c11111a11v1x11zz1rt4wf7cn/?p=469',www.4489.cn,www.xpj9821.com,香港大众论坛,WWW.77111.COM,3311055com,中文字幕本无吗,www.404543.com,www.sha2002.com,15o75.net,www.534cc.com,0166.com,azxcvbnm,WWW.98025.COM,hinews.cn,243678.com,www.902826.com,nyhz1539,www.179666.com,www.8303.com,www. miya199.com,a11177,m.g3055.com,www.760000.com,bmw8049,wwwvnsr4888com,www.nb445.com,WWW.6849.COM,wuhui02111,zhao98,wwwwwwsb279com,yahu76com,848ggg.cc,mg7260.vip,www.7700500.com|

yb6698vip,www55245577com,www.1779020.com,yabo9911.vip,131452062asd,www.pj373.com,www 98k.com,www.55jxf.com,ks4215.vip,www665537acom,m.76029.com,www.82558.com,nxgx,wwwlsls222com,jiahe222.com,http:/ /vip.smaeer.co,www.161760.com,www.long988.com,a78986011,www46426com,www55598sssscom,www2382bfa999com,ld0088com,hg2956com,caa158123,16823.com,w777777,snow90,www.4777.com,www.abab.com,WWW.56.COM.CN,1819172194@qq.com,www.6186.com,4amgj.com,liuqiao,wwwhg796com,www.82444.com,www.msc803.com,www.youjizz0.com,www.222xq.com,875533com,xieyu,www.js71999.com,duanxiaodon,wwwlsntbzy16com,ya1231,www.4358.pw,www.6335888.com,wwwtt111888com,www.9170106.com,www.jusedh.com,c2639471110,777300.com,www.5874685.com,fun88.com,80887.com,www.81849c.co,laohu96.vip,fedsp8,90ttt最新网址,www.999345.com,ttsslife.com,448855com,yuanweiwa,hg6427com,ks3514.vip,2546n.com,www.ggg43.com,www.73765555.com,www.62ey.com,绳艺帝国,xijuen36,3705.cc,wwwsaojjcom,wang22,www.39w66.com,ag9098vip,www231231com,wwwk6755com,www.8hcp234.com,www.16633005.com,swj48.com,mgyouxishoucun100%,aqq5208899,mkmkmkmk,WWW.TYC00.COM,cjin1125666,ccqt1371056,8006026.com,11793994,www.9530024.com,www.1116613.com,wwwtbb47com,www-anquye-com,821277com,wwwcc143cc,www.74747.net,www400888fcom,1801922852@qq.com,www.867bb.com,vip.com,liudangxi,www.365888ylc.com,wwwkj360com,75365365com,wwwmsc50net,www.254904.com,wwwchinaxlnet,39398694@qq.com,www.pjvip4444.com,www80983bcom,y7067.com,www87423com,www.v3.app,0142.com,zzz0020,9065777com,www.219384.com,877858com,vi95611bcom,www.07705536.com,wwwsun923com,www.xg018.com,m.csh666.net,zy1116,www.9857232.com,www.www.sg587.com,www.hg0605.com,421658com,www.xg77.com,hg0724com,cp0399com,4866a63,www.xxf111.com,33477.com,tjm0908,14526161,www.hjc8net.com,japan.girl.tube,15045.com,9892.cc,www.riaoao7.com,ag84693,www.712kb.com,jyj9999,942hs 网址,xq542.com,66t888com,WWW.HHH469.COM,www.bk7788.com,www.hf929.com,a1170449173,www.671425.com,hf.79199.com,83938541,www.xpj8974.com,www.df866.com,zitanmeng,www.gzbwzdh.com,ribentvvivodesoumei,www.444kk,m.196601.com,long9174com,c788hb,bei518,wwwyl336com,WWW97YEYECOM_WWW.97YEYE,COM,www.12345xpj.com|

以上会员名单排名不分前后

相关文档

18版高中数学第二章平面向量6平面向量数量积的坐标表示学案北师大版必修4
18学年高中数学第二章平面向量6平面向量数量积的坐标表示课件北师大版必修4
18版高中数学第二章平面向量6平面向量数量积的坐标表示课件北师大版必修4
2017-2018学年高中数学 课时作业18 平面向量数量积的坐标表示 北师大版必修4
2017_18版高中数学第二章平面向量6平面向量数量积的坐标表示课件北师大必修
18学年高中数学第二章平面向量5从力做的功到向量的数量积教学案北师大版必修4
18学年高中数学第二单元平面向量2.3.2向量数量积的运算律学案北师大版必修4
2019-2020学年高中数学 课时作业18 平面向量数量积的坐标表示 北师大版必修4
18版高中数学第二章平面向量5从力做的功到向量的数量积二学案北师大版必修4
18学年高中数学课下能力提升(二十一)平面向量数量积的坐标表示北师大版必修4
学霸百科