当前位置:首页 >> 数学 >>769898.com

www.5160088.com:最新-2018高中数学 2.4.2平面向量数量积的坐标表示、模、夹角教案 新人教A版必修4 精品

www1952com 67axax最新域名 www.6866.com www.5661.com www42015com www.4411b.com juanminghuangtxtxiazai

qwpk wwwtt7899com msc2000.com www.daidaigui.com www9929lllcom www.181701.com ub8fun

2.4.2 平面向量数量积的坐标表示、模、夹角
教学目的: 1.掌握平面向量数量积运算规律; 2.能利用数量积的 5 个重要性质及数量积运算规律解决有关问题; 3.掌握两个向量共线、垂直的几何判断,会证明两向量垂直,以及能解决一些简单问题. 教学重点:平面向量数量积及运算规律. 教学难点:平面向量数量积的应用 教学过程: 一、复习引入: 1.平面向量数量积(内积)的定义: 2.两个向量的数量积的性质: 设 a、b 为两个非零向量,e 是与 b 同向的单位向量. 1? e?a = a?e =|a|cos?; 2? a?b ? a?b = 0 3? 当 a 与 b 同向时,a?b = |a||b|;当 a 与 b 反向时,a?b = ?|a||b|. 特别的 a?a = |a|2 或 | a |? a ? a

a ?b 4?cos? = | a || b | ;
3.练习:

5?|a?b| ≤ |a||b|

(1)已知|a|=1,|b|= 2 ,且(a-b)与 a 垂直,则 a 与 b 的夹角是( A.60° B.30° C.135° D.45°



? (2)已知|a|=2,|b|=1,a 与 b 之间的夹角为 3 ,那么向量 m=a-4b 的模为(
A.2 二、讲解新课: B.2 3 C.6 D.12



探究:已知两个非零向量 a ? ( x1 , y1 ) , b ? ( x2 , y 2 ) ,怎样用 a 和 b 的坐标表示 a ? b ?. 1、平面两向量数量积的坐标表示 两个向量的数量积等于它们对应坐标的乘积的和.即 a ? b ? x1 x2 ? y1 y 2 2. 平面内两点间的距离公式

| a |? (1)设 a ? ( x, y) ,则 | a | ? x ? y 或
2 2 2

x2 ? y2

.

(2)如果表示向量 a 的有向线段的起点和终点的坐标分别为 ( x1 , y1 ) 、 ( x2 , y 2 ) , 那么

| a |? ( x1 ? x 2 ) 2 ? ( y1 ? y 2 ) 2

(平面内两点间的距离公式)

向量垂直的判定 设 a ? ( x1 , y1 ) , b ? ( x2 , y 2 ) ,则 a ? b ? x1 x2 ? y1 y 2 ? 0

两向量夹角的余弦( 0 ? ? ? ? )

a ?b ? cos? = | a | ? | b |

x1 x 2 ? y1 y 2 x1 ? y1
2 2

x2 ? y2

2

2

二、讲解范例: 例 1 已知 A(1, 2),B(2, 3),C(?2, 5),试判断△ABC 的形状,并给出证明. 例 2 设 a = (5, ?7),b = (?6, ?4),求 a·b 及 a、b 间的夹角 θ (精确到 1o) 分析:为求 a 与 b 夹角,需先求 a·b 及|a|·|b|,再结合夹角 θ 的范围确定其值. 例 3 已知 a=(1, 3 ) ,b=( 3 +1, 3 -1) ,则 a 与 b 的夹角是多少? 分析:为求 a 与 b 夹角,需先求 a·b 及|a|·|b|,再结合夹角 θ 的范围确定其值. 解:由 a=(1, 3 ) ,b=( 3 +1, 3 -1) 有 a·b= 3 +1+ 3 ( 3 -1)=4,|a|=2,|b|=2 2 .

记 a 与 b 的夹角为 θ ,则cosθ =

a?b 2 ? a?b 2

? 又∵0≤θ ≤π ,∴θ = 4

评述:已知三角形函数值求角时,应注重角的范围的确定. 三、课堂练习:1、P118 面 1、2、3 题

1 2、已知 A(3, 2), B(-1, -1), 若点 P(x, - 2 )在线段 AB 的中垂线上, 则 x=
四、小结: 1、 a ? b ? x1 x2 ? y1 y 2 2、平面内两点间的距离公式 3、向量垂直的判定: 设 a ? ( x1 , y1 ) , b ? ( x2 , y 2 ) ,则 a ? b ? x1 x2 ? y1 y 2 ? 0 五、课后作业: 《习案》作业二十四。 思考:

.

| a |? ( x1 ? x 2 ) 2 ? ( y1 ? y 2 ) 2

1、如图,以原点和 A(5, 2)为顶点作等腰直角△OAB,使?B = 90?,求点 B 和向量 AB 的坐 标. 解:设 B 点坐标(x, y),则 OB = (x, y), AB = (x?5, y?2) ∵ OB ? AB ∴x(x?5) + y(y?2) = 0 即:x2 + y2 ?5x ? 2y = 0 ∴x2 + y2 = (x?5)2 + (y?2)2 即:10x + 4y = 29

又∵| OB | = | AB |

? 7 3 ? x1 ? x2 ? ?x 2 ? y 2 ? 5x ? 2 y ? 0 ? ? ? 2 或? 2 ?? ? 3 7 10 x ? 4 y ? 29 ? ? y1 ? ? ? y2 ? ? 2 ? 2 ? 由
7 3 3 7 3 7 7 3 ( ,? ) ( , ) ( ? ,? ) ( ? , ) ∴B 点坐标 2 2 或 2 2 ; AB = 2 2 或 2 2
2 在△ABC 中, AB =(2, 3), AC =(1, k),且△ABC 的一个内角为直角,求 k 值.

解:当 A = 90?时, AB ? AC = 0,∴2×1 +3×k = 0 ∴k =

?

3 2

当 B = 90?时, AB ? BC = 0, BC = AC ? AB = (1?2, k?3) = (?1, k?3)

∴2×(?1) +3×(k?3) = 0

11 ∴k = 3

当 C = 90?时, AC ? BC = 0,∴?1 + k(k?3) = 0

3 ? 13 2 ∴k =

精品推荐 强力推荐 值得拥有


以下是今天幸运会员获奖名单

www.8698553.com,oynbbj,hongyanxx,www.cp31.com,2000ee.com,www.7244.com,www.setoutouyao.com,www.5678.dw,www.jh8058.com,coniok,www3236588com,www.aisedao11.com

chaopengxiazaiyemianhuohu,ag1922cn,www148tucom,www0897com,5hg1088.com,agks1569com,ryc38.com,wwwnetflixcom,www.extremeseksfilms.nl,www.8841017.com,rqs777,www.c24d.com,www.612555.com,www.bbs.cntv.cn,97yes,3424.win,hg4115com,帐号,www.sese9.com,l32689.net,www.353777.com,www.00271com.com,www.wm002.xyz/?m=vod-play-id-3944-src-1-num-1.html,www.opsun,www.092009.com,www.jp0000.com,wwwpj789999com,lhh880120,qy2817vip,yth096.com,www.et502.com,1627816471@qq.com,aizaizuotianxiaoshuo,879jjcon,juren35,www.10383.com,www.191670.com,www.1111qw,www.4419h.com,58555com,www.laok.cc,www8877mmmmcom,wwwbibovipcom,4832391,www.2222ye.com,31ll.com,liuyaqiny,www.6428.com,www.jsdc807.com,www.hg5750.com,ggyy930,dgdyrb,www.ag88md29.biz,www99111cccom,大港贴吧,yabo3904.com,wodenüwangjiejietxtxiazai,bet36579.com,hg0327.com,www444887com,lijun7878,WWW.228888W.COM,czsp22.com.,www.sedy,WWW.TS898.COM,28111mcom,2695515986@qq.com,zhang123,xpj0844.com,www.1797799.com,yb4750.com,www.f01158.com,czj3333,www.59382.com,www.aabbav.com,www.8996xxx.com,56733m.com,www.xj9998.com,www.918euu.com,www.907aa.com,www.hg1783.com,wxp0828,56807.com,wwwmgm8535com,zunlongwangzhidenglu,55331y.com,188luckcom,yixingjiashouye,www.9448v.com,876878.com,www.vnsr2018d.com,wwwyf3789com,www.141933.com,42444神算一码,98088.com,891662com,wan4557.com,www00852003com,672866.com,www40083366com,tttrrrttt,www.6623t.com,pay4809.com,m.ks6871.com,www.jiaoshoujiazulin.com,wwwys5888com,www.703ii.com,www.22w33.com,dashenyule,www26333com,www.yuyu123.com,www67nnncom,wwwh95661111com,huangjiayulezaixianzainazhuce,www.678.hk,www.wxc1155.com,www310111com,AQDAV. com,www.pj0997.com,wwwylg051com,www.718160.com,qin0331,www.38sx.com,wwws8s484me,dd6866.com,wwwra5898com,www.080DV. com,wwwdhy323com,kkkk7777,892215com,04311.com,www3X444cc,www45489.com,893104667@qq.com,www.vip.p439.com,www.ssc671.com,zhuweiming,www.JDB6666.COM,www.00271,18105085859,wwwbet02000com,xiaohongxiu,www.hg773999.com,bao578,chenjiachuan,nxgx动漫,oumeigaoqing69vivo,jsc0000com,www.pj99l.com,www.vnsr.com,788703,www4926com,www.pj92777.com,jackwen88,5217,www.111qqq.com,wwwtc5588com,355ff.con,www.18686.com,yabo5971com,www.dj666999.com,hg7878.com,www.zhupa.com www.maomi.com,36373333p,liusanhong,wwwl9899com,hg257.com,2666y.com|

www.kaifan365.com,quanminsaima,yb5742.com,wwwhg4842com,189887.com,www.623ww,825511com,早乙女露依种子,www.677374.com,152ku新网址,www.2424ww.com,178345.com,hg503300.com,66ys.com,855066com,erswdgsdf,sd33333.com,曂片网 影院,xqb7896,www.576635555.com,www8828bbcom,ezs348,lh0296.com,www.www.ttt542.comwww.ttt666.com,www.hg1637.com,wwwyl5565com,9002846.com,fun464,807.net,www.am915.com,www089163com,626950.com,e00001,www.hd189com,xiangwei18,www995505com,liujiajun,www9680gcom,www.jimei5.com,www552553com,www.306xx.com,pk959com,wwwe7720net,033005.com,www.soccerbar.cn,www.325,hg168175.com,www.2605579.vip,www.jing254.com,www.532433.com,www81849icom,yu0627,www.33qqbb.com,guangyan0,www.999948.com,www.689777.com,wwwhg5740com,agc413.com,jiafaguizuxiaoshuo,www.091sb.com,899537com,www.54709.com,5&7777.com,gjfskyxh.com,qy3759vip,7098.com,zsx123,wwwyhvipco,406999.com,wan4236.com,WWW.660se.COM,www.722666.com,www.ab673.com,dubopojielu,www.90363.com,vns2896com,huomeigui,www.2011.com,www935432com,WWW.49500.NET,www.mmm883.com,bet6694com,www.48284444.com,www.cun08.com,www.hm007.com,sb11,55268uu.vip,www.rrrr0042.com,wwwtjchemsjcom,141hongkong,www.sinnistar.com,www96kpw,www.91uu.sita,miya665. com,www.fc2cn.com,wwwh4776com,wwwhg5543com,48884.com,www.btset.com,av4499com,www.399699.com,wwwkk737com,www.p9293.com,www.9886f.com,www66am1100com,www.m.hg73488.com,uyedtrf,www.yinhe47.com,sb8801.com,www.1105877.com,p00j.com,www.188917.com,www.ssd0000.com,rb15.com,www.szs99.com,www.ww,wwwalibetin,bet0091com,860477com,xiqi77521,899238com,wwwba0288com,761ysb.com,www008ttcom,qibilu,wwwso155com,波多野结衣野2018,xjw258,this82,wwwvns98765com,www.206sihu.com,WWW.1188D.COM,hg2343com,WWW.57257.COM,yabet9236com,868783com,www.52iii.com,www.g5859.com,040104.com,105.net,www.xgsm.com,www.00755.com,www.lushen.com,www.yinhecc.com,www.cccyy.com,www7124acom,www7970898com,qyy4839com,qyy8764com,llwww.858989.com,www55584com,www.99663.com,www.hg6346.com,3769876,wwwsu1898com,iol63536,niuweikang,wwwbmw3533com,wwwra373com,wwwg6222com,ttcv3,琪琪视频在线观看,lehu2363com,yb3021com,www.hg3809.com,wwwhgw8999com,www.itb442.com,wwwxpj4229com|

lin768,www.407uu.com,hgw777.com,www.340096.com,agks62.com,www.dr4g0nvip.com,www.778897.com,22898.com,www5575com,wwwhg0621com,8889298.com,lh2703.com,egecao8.com,jihua,yh8690.com,866789com,WWW.HYFZK.COM,www.690253.com,ni0811wo0904,wwwxpj3394com,wwwa9666com,pornwatchers.com,wo.com.cn,cp999.com,112com,sanjikanjianmeinvtuoguangyifudianying,www.t66y. com,www.hg90177.com,www.j835.com,大桥miku,491666.com,www.95178988.com,647755.com,280abc.com,wwwk077com,www.5829yh.com,wan9141.com,WWW.71817.CN,www.cxcp151.com,Spectre x360拆机,h65as,vns4760com,bmw999.com,8391lb.com,zaos,860760.com,ag1823com,js888500com,865845558,www80s.cn,www.g68868.com,www.7764q.com,wwwyccp44com,www.symama.com,www.62nnnn.com,xg66511,www.blr060.com,qy1047com,www.da000.com,18dz pw,ab1029.com,45789.com,zs406.com,9900f最新域名xyf,xpj3359com,www.510215.com,7830f.com,lh2201.com,164.net,darupennaishuizhibo,f4u7864y,sepapa888,wan1779.com,WWW.33668.COM,www.518200.com,www.js00021.com,46288com,www.531005.com,www.pj6058.com,54907z.co,www.19nf.com,1198yl.com,ks8948com,www.273suncity.com,ww147258,nxyinda.com,www.j045.com,3648821.com,www.96899.com,www.72bb.com,cash-1688.net,www.5936h.com,藏姬隔导航精品,86697lcom,379504585,www993336com,www.00233.com,www.6659y.com,js8531com,110110kl,www8836com,www.15816.com,www.6865c.com,67896789.com,www.58k7.com,632415678@qq.com,bet154.com,yb070.com,rcpla,ttqp393.com,www.2v66.com,hg5892com,www.hg8879.com,3891046.com,766987.com,76678.com,dongling,Www. miya997.com,wwwqknet,892893com,www.5023112.com,402599.com,www.3889nm.cc,4955j,www.21511r.com,www.b75875.com,fdjk5389,4ppav,www.733111.com,www.8844go.com,399878.com,9486-34,wwwvv008com,菠萝蜜无限制视频,agc749.com,www.yyzz6.con,www.a666666.com,m.bet80000.com,wwwyf4488com,wwwhappy778com,www86662com,www.6277088.com,shuru88,wwwqiuxia,www.ks5000.com,wwwlbvip8com,www4231bcom,www.33355599.com,1213699com,www.6633,www.552305.com,hahagan,ydlk456,www.5785e.com,www.34266com,www.8665123.com,www.1239160.com,www.7886555.com,agks6967com,www393838com,www.4135.com,yb0918.com,34211..com,www.665143.com,9687.com,www.hg6685.com,75uy666,czsp11. com|

88833-9,jinzhuyue,1191731709@qq.com,9204hu.com,MiYa177.com,qq98765,8308lb.com,www.873678.com,www.13seba.com,www.667zs.comwww,www.ag7008.com,www.181js.cc,www.mao4848.info,study.xuexi.cn,zf9527,lycp34,WWW.720321.COM,151855571,www3506xcom,wwwxpj6aacom,苍苍影院在线观看免费体验版,www.9424.com,www.897bb.com,wwwxin6622com,www31caocom,dd11hh.com,wwwHG7134COM,www.991238.com,www.60957700.com,www.www.bj1111.com,www.hga227.com,75xh.com,www.6888111.com,www.16204.com,tk368.com,zc4848com,fuf4444.com,www.3488035.com,yabovip5511com,663388,5474bet,www.agent.hg7113.com,6850.win,xg43.com,www.hg6660.com,lovebetlove602.com,2256bb. com,xpj8134.com,avsow.com,hg624.com,www.4237tt.com,362838com,www.72599.com,02887l.com,kaijun,www.6624h.com,www. ddd 809.com,bet9330com,WWW.33533.COM,www.yzyz04.com,www.369774.com,www.65111.com,2061143,4455by. com,mg2812.vip,www.183883.com,zyy1688,www.3344pw.com,2030lu.com,dsadsada@126.com,866550com,www.381555.com,www.sun1855.com,boweimech.com,52105210,chuwei,007098.com,wwwq8899com,www.v800222.com,www.ra6788.com,wwwlhc123hk,www.13322.co,wwwzuan6633com,www.et348.com,siguashipin18jinzhixiazai,www.467246.com,www.vbet362.com,9000yy.com,www968jscc,www.sb976.com,www308ee.com,www.154641.com,www.lehu7088.com,y8988.com,www.83600.com,www.k56.com,ananlfeng.com,www.avav,bd1606,ag9988.vip,www.6yyykk,qo9uv8d0,bbinyulechengjinshaguoji,9232.com,www.p4555.com,www.803777.com,716659com,www337706COM,www.dz033.com,c2325351233,www.530883.com,715pacom,www.1665a.com,WWW.86,www.43762.com,www.qq554.com,3119.com,pu711在线,www.47nana.com,57ks.net,www.9117869.com,514msccom,ag4072cn,8785lb.com,www.bet311.com,893338com,lyg0022,jinshawangluotouzhu,www.730678.com,www.mobile181hd.com,m.9189aa.com,www.dafa777.com,www.1744k.com,www.78222.com,mm606.com,259tk.com,yy707y,www.ddd9520.com,www.sdkct.com,langying11,www.1429p.com,piaoling,www.3984.com,www.63699.com,www.v868.com,www.369450.com,qqyewu.cpm,www.118394.com,wan1930.com,abc5555,www.nedh.xyz,www.3322.org,WWW.362L.COM,wwwpj12888com,www.hg2390.com,www.39390.com,www.296hu. com,kai95980,www.703266.com,www.585808.com,www622677com,wwe5886,www.wns500.net,www.kxm13.com,www9415com,xpj626.com,www.923654.com,www.bg849.com|

以上会员名单排名不分前后