当前位置:首页 >> 数学 >>www.3388203.com

1613.ag:高一数学课件-高一数学课件:平面向量数量积的坐标表示6 最新_图文

www.040661.com jbb29.cc 5702bet www136546com hg165.cc 10050558 wwwn5511com

www.hengjingkj.com www.8808000.com www.6855.com www.qudou1216.com whxs630728 www.swjs008.com w6637.com

高一 数学 平面向量数量积的坐标表示 王人伟 北航附中 播放时间 6月9日 1.已知两个非零向量a和b,它们的夹角为θ,则 a· b= a b cos θ . a· b称为向量a与b的数量积(或内积). 2.数量积a· b等于a的长度 a 与b在a的方向上的 投影 b cosθ 的乘积. 3. a⊥b a· b=0. 4. a· a= a 2=a2. a· b 5. cos θ = a b 6. a· b≤ a b . . 复习题1 已知: a =4,b =5,a· b=10, 求:a与b的夹角θ. 解:设a与b的夹角为θ ,则 a· b 1 cos θ = = 2 , a b θ =60°. 复习题2 已知:A(2,1),B(3,2),C(–1,4), 求证:?ABC是直角三角形. y 分析:先画图, 从图中可知, ∠A应为90°,为证明∠A =90°,只需证明 C B A O x AB · AC=0. 复习题2 已知:A(2,1),B(3,2),C(–1,4), 求证:?ABC是直角三角形. 由AB· AC= AB AC cosA 可知,为了证明AB· AC = 0, C y 需先得出 cosA = 0,需先 证明∠A为90°,而这正是 A O B x 最终要证明的结论. 5.7 平面向量 数量积的坐标表示 在坐标平面xoy内,已知a=(x1, y1),b= (x2,y2),则 a· b=x1x2+y1y2. 即 两个向量的数量积等于它们 对应坐标的乘积的和. a· b=x1x2+y1y2 证明:设x轴、y轴方向的单位向量 分别是i、j,则 a· b=(x1i+y1j)· (x2i+y2j) =x1x2i· i+ x1y2i· j+ y1x2j· i+ y1y2j· j =x1x2+y1y2. 已知:A(2,1),B(3,2),C(–1,4), 求证:?ABC是直角三角形. 证明: AB=(3 – 2,2 – 1)=(1,1), AC=(– 1 – 2,4 – 1)=(– 3,3), ∵ AB · AC=1×(– 3)+1×3=0, ∴ AB⊥AC. ∴ ?ABC是直角三角形. 由向量数量积的坐标表示,可得 (1)若A、B坐标分别为 (x1,y1)、 (x2,y2),则 ( |AB| =√(x1-x2)2+(y1-y2)2 |AB|2 = AB· AB = (x1-x2)2+(y1-y2)2 a ⊥b B x1x2+y1y2=0 (x2,y2) x1y2-x2y1=0) ) y (2)设 a=(x1,y1),b= (x2,y2),则 (a∥b (b≠0) A (x1,y1) x O 例 1 已知a=(1,√3 ),b=(– 2,2√3 ), (1)求a· b; (2)求a与b的夹角θ. 解:(1)a· b=1×(–2)+√3×2√3=4; ( 2) a = √1 +(√3 ) =2, b =√(– 2) +(2√3 ) =4, 2 2 2 2 cos θ = a· b a b = 4 =1 , 2 2× 4 ∴ θ =60? . 例 2:已知a=(5, 0),b=(–3.2, 2.4), 求证:(a+b)⊥b . 证明: ∵(a+b)· b = a· b+b2 =5×(–3.2)+0×2.4+(–3.2)2+2.42 = 0, ∴ (a+b)⊥b . 例 3:已知:A、B、C三点坐标分别为(2,0)、 (4,2)、(0,4),直线 l 过A、B两点,求 点C到 l 的距离. y 分析一:如图, 为求CH长,由 CH=AH-AC可知,关键 C 在于求出AH. B l 由AC· AB的几何意 义,AC· AB等于AB的长度 H 与AC在AB方向上的投影的 O A x 乘积. 所以 AC· AB=AH· AB. 解:AC=(0 – 2,4 – 0)=(–2,4), ∴AB AH = == (1(2 , 1). = (4(2 –m 2 , 2m –)0) , 2), y AC· AB=–2×2+4×2=4. CH=AH-AC=(3,–3), C ∵AH与AB共线, 2+(–3)2=3√2 . CH = √ 3 ∴可设AH=mAB=(2m,2m). B l x AH· AB=4m+4m=8m. 即由 CAC· 点到直线 l 的距离为 AB=AH· AB,得 3√2 . m= 1 2 . H O A 若能确定H点坐标, 分析二: y C B l CH长就易求了. 为定H点坐标(两个未 知数), 可利用H点在 l 上, 及CH⊥AB这两个条件. H O A x 练习:1.向量a、b夹角为θ, (1)a=(3,-2),b=(1,1), 1 则a· b=_________ ,cos θ =______. 26 |a|=√13,|b|=√2 (2)a=(-1,2),b=(2,-4), -10 ,θ=__________ 180? 则 a· b=_______ 2. 已知?ABC三个顶点坐标A( 1 ,4 ), 3 3 B(-2,3),C(0,1), √26 求证:?ABC是直角三角形. 小结: (1)掌握平面向量数量积的坐标表示,即 两个向量的数量积等于它们对应坐标的 乘积之和; (2)要学会运用平面向量数量积的坐标表 示解决有关长度、角度及垂直问题. (1)P121 练习; (2)P121 习题5.7 第1、2、4、5题. 今日 作业

以下是今天幸运会员获奖名单

www.bn8899.com,www.11o11o.com,wwwjs9335com,WWW.3421.COM,www.jinniu03.net,WWW.55SWZ.COM,www.hk,www.0066bb.com,www07272com,om5908,min8888,agc656.com

612555.com,www392323.com,WWW.51538.COM,www.56988p.com,www.3644o.com,www628567com,www.bet7160.com,441261,16211258,18670093008,www.117487.com,WWW.166700.COM,10050837,wwwbm5346com,yase999中文,gb1204,www.xieey.com,41139.com,www.282ks.com,wwwb70266com,qwxindao,WWW.AG.HG44555.COM,wwww662678com,2014945286,5678bo.com,yh3497.com,paipaijiaotongdeshipin,www5248com,glin,www.404ww.com,yj918.com,www.1708999.com,13044324777.com,363bomao.com,mmtx44.com,www.zzdfxy.com,www3467dcc,WWW.ALALI44.COM,cliu24,wwwjsp00com,www.4491.com,www.kanzhelu.com,jimuerziluanlun15p,10050876,9839.com,biyingyulewangzhan,www.668999.com,huangshangdexiaomengchongtxtxiazai,dcy94,www47so,www.syjy.5u5u5u5u.com,www.984920.com,www4577ocom,www.hgw2017.com,8877b.h81y.com,c1989xiao,q123456,www.076000.com,wwwgz0011com,ok99okcom,cwy4936,WWW.ED552.COM,www.605v.com,wwwjz185com,www9994mgcom,www. 272mm.com,www.eu998.net,js29567,dhy5519.com,qyy2676com,ag9922.win,zhenqianniuniuyouxi,j9a4n.landong.com,www.909022.com,ag84894.com,yuguo521,www.t180888.com,30833.com,www.97878mm.com,www.bu229.com,WWW.ZD1100.COM,www.xpj886444.com,255tk.com,www.880t,www.526317.com,hubet.yabo77.com,www.8358.com,yb6201.com,1370988709@qq.com,wwwjs9785com,771199.com,6698666.com,zhengfj,bc2030.com,wangtao19881,www888zhenrencom,www.xieyuge.com,cjm111,www.mapai08.com,www.hg9899.cc,lh3396.com,wwwwrm55com,wwwlibo226122com,www.672888.com,wwwuhooballcom,www.570336.com,zb4500.com,00118040.com,iverson,www.563447.com,avtt天堂网com,www.dalu99999.com,www123887com,www.3653656.com,66888.vip,www.bg351.com,www.209214.com,西林吧.百度贴吧,WWW.CAOBIAO456.COM,www.haole18.com,www.3777338.com,1138lb.com,301788.com,wwwrr9013com,www.6856635.com,www914966com,www.76669.com,qifa374com,www8133555com,hlg866.com,m.k831.com,lehu109,www.620593.com,www6498xcom,77755508.com,wwwseqing,gc971.com,6608x,wwwmms263com,www.910474.com,www42227com,www587com,ali888,a884449,www268shcom,8r7stw,www2836515com,www.rb0118.com,hongfa.org,www.ysb3.com,www.www.22jj145.com,chang321,hg52678.com,58557.com,www.83877.com,www.888s99.com,yzy839612,www.054668,www.20088.com,www19fffcom,www56141com,ag8874.win,,www.336057.com,wwwyh7933com,711nncom,mobile.ruyig.com,296011.com|

850675com,www.073666.com,www.1750z.com,eee267,6kkp奇优影院,wwwddh711com,cj788224567,hjr1010,www.yw80606.com,miss520,sis最新地址,www.hg3755.com,www.08817.com,3249.win,yixinyiyi,www.122610.com,rf488.com,hg0469.com,22nsbcom,huangzm001,wwwhg0694com,dongmanmoshilutxtxiazai,www.301pj.com,www.297999.com,Mylive.taoy66.lnfo,goujian,www.51416.com,www.d228.com,ku2mmcom,www.xxx10000.com,www.3351cc.com,www.88627.com,lulukanclub最新,eee67在线观看,9952,1538.bet,lh2703.com,lh9153.com,99036.com,www.507778.com,hhh66kk,wwwagjg6688com,www324366com,www.555979.com,lizaixing,80067373,ez-n.enzuo88,282924284,yuying,www.pj56w.com,www.9996yy.com,88740p.com,www.2019202.com,6879com,2356838548,731028.com,0662byc.com,www.xpj5794.com,www.da3355.com,dingpeng,www.7935q.net,www.369yz.com,asd44444,wwwbet6156com,WWW. AMGYY.COM,yt359.cnm,jiuzhouguojizhucesong39yuan,www.9cdz3.com,850431com,www.303680.com,41529.com,www.21365uu.com,www657aacom,www.980777.com,3773.com,wwwr5888com,WWW.DW995.COM,banfang,w369,www.178zzz,yb8324com,9832cc,caa32740323,kb3535.com,www.6147.com,21378844.com,bet6301com,WWW.BET203.COM,ss30000.com,www.3085.com,20464,www.567dog.com,www449hcom,8810,www.79wx.com,yinxx,www. vv256.com,www.8818h.vom,vns7766.com,ks8821.vip,ks6630.vip,jbb071.cc,www.17077.com,www.senb4.com,www919zzcom,www.333678.com,6622vnscom,googlebaidusogouso.com,nhzjl,www.468860.com,wwwcp739com,www.3459f.com,www.232739.com,www.16788.cn,666kaac0m,www.7777660.com,wwwhg8816com,www918609com,yindongxue,402y1,www.123123456.com,wwwlong397com,zyj223,www.09577.com,www.37799F.COM,www.819js.com,www78898COM,jzztm.com,欧美同志高清vivoeso,yb5904.com,66pp136.com,764609com,7492com,gm133.com,827921com,www.h26.com,www.28282325.com,jiaren658,omeishunvduozhi,nvxingdeshuangshuangyingyuan,woai22.com,hk6hcom,www.drf0713.com,22296jacom,WWW.V38.NET,www.blm008.com,www.3mgmwww.com,552uncon,www.xpj6593.com,www.6088040.com,958500.com,bbbbb.com,www.87aaaa.com,hh66kk. com,www30979com,www.9896w.com,yh6929.com,0698.bet,qyy3481com,wwwcq704com,www.bbs.755755.com,WWW.TK5566.NET,fang1234,2061311.com,www.813777.com,www.2100cq .com,chengrenyingpian,333gpk.com|

www.hg80879.com,www.1381083.com,WWW4455RACOM_WWW.4455RA,COM,221mi.com,www64988com,WWW.883699.COM,www.1113015.com,www.8905f.com,22789365.com,www.yasezz2 .com,41sssssssss2s2s23ss121ssssssss21ss1ss4ss2sss1s93.rt4wf7.cn/soft/CESU_WS_API_v2.12.pdf,bbs.kswinwin.com,se448.com,235111,www.16972.com,www. 7898tt.com,www.sd9998.com,t2206.com,jm6868.com,www.xnews.com.cn,www.6696r.com,yb1191.com,www.4hu46.com,www.10130.com,qyy1019com,www.6858c.com,WWWJC400COM,jjs11com,www.42mscc.com,www.576485.com,www.hbke.com,aomenbalirenyouxiwangzhi,m.tb.cn/h.3xml2FU,c1313131361,http://www.xte87.spa,www.4499.com,cesu shangdu.com,www.wyl360.com,www.tuyimm.com,www.12222hh.com,ks10.vip,100.com,080079.com,412c2,92584.com,www.58077.com,www.bj045.com,wy0915,xinlingdian,201705.scldh.in,zhu123123,tqqsst,www.280629.com,www.s8s345.me,785785.com,69uuu. com,www383802com,www.17828h.com,cailifun88,www105050com,77075sscom,bakp92,www.jy002.org,WWWSNNFSCCOM_WWW.SNNFSC,COM,gaoshou,long1768com,468373com,34om.com,renqing,www.968444.com,234aq,www. 230Cd,www.2002cn.com,www948332com,www22sblivecom,wwwgrcpcom,www.44xmxm.com,133223,xiaohong368,www 87bebe. com,ag4949com,yb0811.com,www.639010.com,www.426088.com,www..5k55.com,wwwwww.5151淫/favicon.icn,8978vip,14388.net,as3288.com,www.hg18000.com,www.8658365.com,WWW883799COM,c159965376,wwws8s555com,wb1840com,12223w.com,zjt123,5856vv,www.984895.com,www635336com,wwW.2441com,csu5796,3144mm.com,zgzlhk.com,www7275,www.be9988.com,7022bet6.com,wwwjs16188com,www.91bbbme.com,768768.com,www.598051.com,staticqspfwcomxf2019indexhtm,cbcb098.com,wwwbm2803com,WWWVNS99COM,xpj5,xpj3530.com,renyushoutupian,yhy-bj@163.com,27365111,www.ddse20,q3112,yb0541.com,www39552525com,1261976130,www.2222.com,aa.958227.com,https://WWW.704.aacom,xpj101.com,69fadacom,175444.com,www.xed005.com,898447com,WWW93PUSCOM_WWW.93PUS,COM,wwwccc381com,0003s.com,ag2756vip,www.33355006.com,qweasd777,49533.com,www4018dcom,www63555sscom,www.w3366mp3.com,www.cdjipin.com,www.drf0812.com,www.33os.com,badiaoneikudapigudongtu,wan6299.com,m.68979c.com,www.426326.com,www.6620yy.com,www.ylgzxd.com,zl5413com,hubet.yabo623.com,qifa960com,www.yh1606.com,ezjsl.xadljc,www.hg4288.com,zhahyan8899,965949099,dragon,748MSC.COM,wwwjdb9999com,zuoyu520,www.9911.combkwww.xy,qtqt111,www.7754222.com,www.14638.com|

www./jj129.com,www.pj555023.com,www.uf8813.com,fafa661,www.363838.com,and.o@sohu.com,2632.win,touyouvb1231,www.90111.com,2802644485@qq.com,seyeye点击,xpj9797com,www.jey44.com,www.35510.com,ag6366cn,1387075,WWW.HG618.COM,www.ybh7777.com,yabovip8357com,www.pp6s,www.946bv.com,site988,www.152zz.com,lehu396,yh6963.com,www90108com,www.tutumv.c0m,www.hhh234.com,wwwyh4235com,www.jqb09.com,yes5789,WWW.TK856.COM,WWW.5878.COM,869710com,qifa915.com,rongyaomeitiansong6yuanjiujijindebuyu,www.1032.com,190256.com,www.866222.com,www.5g394.com,xpj2737com,8114j.com,www62223015com,yb9087com,www.erolv33.con,www.652js.com,www.9956t.com,832ks.net,www.4567hg.com,wwwww-64000com,hg2808ff,js4634com,www.201suncity.com,www.99205x.com,siyu88.cn,www.617.com,www.503742.com,www.hg7860.com,www.hg1088.cc,www.cp88904.com,lehu5252com,www00793com,wwwzqceocom,ke168.com,sepapa88cm,xpj0264.com,www.4040xx.com,www.mg8169.com,WWW.MG7777.COM,wwwbg875com,ag89967,k88883com,g3777.tv,88809com,77802g.com,yabet7049com,口袋影院,899969com,www.xzayy.com,www.un99.com,www.yh5413.com,kx678,xy666,npxdy123,597700194@qq.com,ks6828.com,www.55135.com,www.98msc.com,bai9911com,wsc128186,wwwpj4456com,qwe1123,www.bmhssc.com,www.hg3131.com,www.277.net,www.xpj162.com,jka8uak,846dd.com,www.6217.com,545776734,a3812854,youdew88zhinengshoujixiazai,www.m.7676345.com,www51978com,www.g5544.com,www.rk1155.com,www356118zcom,www.7224.com,53kkk,15177274774,2127050.com,xh8206,www.918hht.com,www13699lcom,170726696@qq.com,www.3024kk.com,www.087w.com,qyy3021com,www.ks2375.com,www.888789pj.com,byliangjun,chinesedemfom1346,bm5435.com,WWW.604MSC.COM,203dabao,www.834987.com,www33152250com,http://m.sodyy.com/,www.hy8869.com,www.6660944.com,tingtingse,www49319net,youfa9152com,www.9885p.cow,jb7761,1556573083@qq.com,kj719com,12044,com,zd6517com,www.79287.com,2107. com,7898882.com,37770712,爱CIA,783900.com,彩色85556图库 香港,qyy9996com,www.3522w.cc,yabovip1725com,zichao,www.hao123.com.cn,wwkk22,2525cheng,4688888com,www189msccom,www.688an.com,my6bcom,huanw18,uyvcd.com,www688878com,wwwcd2212123com,WWW.NTYYBJ.COM,mibk888,5627t,wwwhggj4488com,www.974597.com,nuoya667.com,www.bbs.hkyzx.com|

以上会员名单排名不分前后