当前位置:首页 >> 数学 >>aoyousky

7490lb.com:精品(北师大版)高中数学必修四:2.4《平面向量数量积的坐标表示》教案设计

www.mdl99.com vns2069.com www.hg8411.com www018a56com m.w0229.com www79399com www.7276hd.com

www.9679e.com www.5487.com 13428104953 www.am0444.com WWW.UV3OX3.COM 22447712.com 77kp.com

北师大版数学精品教学资料 平面向量数量积的坐标表示 教学目标 1.正确理解掌握两个向量数量积的坐标表示方法,能通过两个向量的坐标 求出这两个向量的数量积. 2.掌握两个向量垂直的坐标条件,能运用这一条件去判断两个向量垂直. 3.能运用两个向量的数量积的坐标表示去解决处理有关长度、角度、垂直 等问题. 重点:两个向量数量积的坐标表示,向量的长度公式,两个向量垂直的充 要条件. 难点:对向量的长度公式,两个向量垂直的充要条件的灵活运用. 教学过程设计 (一)学生复习思考,教师指导. 1.A 点坐标(x1,y1),B 点坐标(x2,y2). =________ =________ 2.A 点坐标(x1,y1),B 点坐标(x2,y2) =________ 3.向量的数量积满足那些运算律? (二)教师讲述新课. 前面我们已经学过了两个向量的数量积,如果已知两个向量的坐标, 如何用这些坐标来表示两个向量的数量积,这是一个很有价值的问题. 设两个非零向量为 =(x1,y1), =(x2,y2). 为 x 轴上的单位向 量, 为 y 轴上的单位向量,则 =x1 +y1 , =x2 +y2 这就是说:两个向量的数量积等于它们对应坐标的乘积的和. 引入向量的数量积的坐标表示,我们得到下面一些重要结论: (1)向量模的坐标表示: (2)平面上两点间的距离公式: 向量 的起点和终点坐标分别为 A(x1,y1),B(x2,y2), = (3)两向量的夹角公式 设 =(x1,y1), =(x2,y2), =θ. 4.两向量垂直的充要条件的坐标表示 =(x1,y1), =(x2,y2). 即两向量垂直的充要条件是它们对应坐标乘积的和为零. (三)学生练习,教师指导. 练习 1:课本练习 1. 已知 a(-3,4), (5,2) 练习 2:课本练习 2. 已知 =(2,3), =(-2,4), =(-1,-2). · =2×(-2)+3×4=8,( + )·( - )=-7. ·( + )=0,(a+b)2=(0,7)·(0,7)=49. 练习 3:已知 A(1,2),B(2,3),C(-2,5). 求证:△ABC 是直角三角形. 证:∵ =(1,1), =(-3,3), =(-4,2). 经检验, · =1×(-3)+1×3=0. ∴ ⊥ ,△ABC 是直角三角形. (四)师生共同研究例题. 例 1:已知向量 =(3,4), =(2,-1). (1)求 与 的夹角 θ, (2)若 +x 与 - 垂直,求实数 x 的值. 解:(1) =(3,4), =(2,-1). (2) +x 与 - 垂直, ( +x )·( - )=0, +x =(3,4)+x(2,-1)=(2x+3,4-x) - =(3,4)-(2,-1)=(1,5). 例 2:求证:三角形的三条高线交于一点. 证:设△ABC 的 BC、AC 边上的高交于 P 点,现分别以 BC、PA 所在直线 为 x 轴、y 轴,建立直角坐标系,设有关各点的坐标为 B(x1,0),C(x2,0), A(0,y1),P(0,y). ∵ ⊥ , =(-x1,y), (-x1)×(-x2)+y×y1=0. 即 x1x2+yy1=0. =(-x2,y1). 又 =(-x2,y), =(-x1,y1). · =(-x1)×(-x2)+y×y1=x1x2+yy1=0. ∴ ⊥ ,CP 是 AB 边上的高. 故三角形的三条高线交于一点. (五)作业.习题 5.7 1,2,3,4,5.

以下是今天幸运会员获奖名单

wangjianli,www.814ab,p6308.com,www.1106.com,www.5855rr.com,www.99553855.com,33spiritcom,www.6115997.com,55125.cn,5555335com,mmtx77,m.84ty.cn

www.028713.com,youfa5186com,hg4788.com,www.fkd222.com,http://www2zzncom,wwwppjj06com,www.18249.com,wct77.com,www.717ww.com,ks3686com,daliziqq@163.com,cboosas,x4244com,694335948@qq.com,ww5574622,www.js1919a.com,www.rrrr11.com,wwwmgm95555com,31826.com,www.wns239.com,33ppqq com,www.980xy,www.88125ww.com,www.lh6618.com,www.eee855.com,c991213.com,c1589266994,www589999com,WWW.WWW.BJ660.COM,www30280dcom,yb2748com,860088,www.js60066.com,www.baxtax.cn,zunyi103.com,871120,7896scom,www377377com,qingqingcaozaixianshipinlian,www.hg0124.com,95zhizunguojiyule,liao110,basiwa.com,www.e8084.com,dcy48,www5004qcom,88894com,www.500xxxx.com,ag.17796666.com,759365com,www56698vcom,kkee88.com,lolhentai net,7781z.com,www.552480.com,ribentejizuorenaicji,h7888.com,810999com,dfc02com,www.6369kj.com,www.youzz.com,www.am663.com,www257com,18050185309,6175cccom,www.lll22.com,nihao,ao1519681333,wwwyh13789com,www.0588g.com,737cc,www.441x.com,www.9696886.com,WWW.HG5324.COM,9960.com,184ff.com,www.7755440.com,www.bifa0023.com,7722dhygwcom,yh9542.com,jiangmu1314,四虎ww224ttcom,aaa32446199,www.68hg.com,www8115com,www.36066l.com,tyc2610.com,www.gzm4.com,yiyitxtxiazai,dj95598,www .992369. com,http.//kuguawujie2015..com,www.yh4645.com,yh9090.com,5677tt@.com,www.343488.com,WWW.FC574.COM,tw58qp,wwwnowscorecom,www6fnet,yesok44,960555.com,27577700.com,ag0207cn,13432382234@163.com,tycjt368.com,wb3120com,www9239acom,www.555989.com,18817266673,js07.net,ttcp8.com,www.by516.com,www.614098.com,87687687@qq.com,www.g3311.com,2020年香港挂牌,www.sogou.com/sogou?query=411s1111211c.rt4wf7.cn/,842777com,qy6295vip,guoneizhenshimuziluanlunshipin,www6882hcom,www7777331com,fdc.fang.com/news/2019-07-01/32775512.htm?wapbottom=zhishi,eeee14,wr1354267182,www.888759a.com,yf710.com,www.782233c.com,www.heng88.com,www.g8751.com,77caca自动跳转新域名,wwwjsdc514com,www.1889710.com,www.5926.com,www.23gr.com,www.lz1122.com,js2553com,www.ho123.net,ibmcom,WWW.ENGHUANG198.COM,youfa6987com,cc27.cn,906msc.com,888134com,WWWHG6134COM,www.g430.com,www.w7488.com,tyc1872.com,pu75999com,wwwmh3888com,7465com,www.940kcw.com,201466com,94yybb.com,wwwlhc,www.09756z.com,为什么290zz看,ph147258,yb5308com,www.10msc.com,www.xpj1414.com,www.11bubu.com,804119com,446413185@qq.com,www.086ee.com,hongyunguojiyulechengluntan,www.74477.com|

www.6666ff.com,www.v03.com,母乳av,www.7711nv,www.3556.com,zzz556.com,tyl1361,83sunbet.net,8080hh.com,www.5651n.com,660156.com,WWW.WWW.188BET.COM,www.167888.com,www000098com,6088.com,www.play855.com,yb3138com,www.669yy.com,WWW.ACAI.COM,vns7418.com,www.v5.com,wwwmh222com,www.767365.com,ag9658com,www.20kv26.com,WWW.TCSY.NET,www.avblg3.com,www.2325g.com,avgle.com,www.133277.com,wvw.606707.com,789se.com,pjf5858,6573.com,yobet817.com,wwwhg8395com,zl1295com,105647.com,www142nncom,linanliang,www.690129.com,wwwmg3511com,交警拦军车被击毙,843398com,185msc.com,www.gdh26.com,www.xin221.com,js3733com,longkaohui@1126.com,83396.com,anneiou,www.cbkccc.com.,www.66450.com,www.686903.com,www.4017.com,bwinyz51,q1w2e3123,帐号,www.343967.com,www.vm953.com,www.df888and188.com,www.4141he,www.jl0009.com,c1443.com,hg7424.com,yh5852.com,WWW.357268.PW,ab4332,lele131,https://www.yrww1.com,518abc,www.x4jdm.com,obo8.net,899883com,www.1366388.com,265bb. com,www.432885.com,www.bl778877.com,4388xchengrenwang,yf267.com,xpj0748com,www.t07.com,www.7o376.net,bet2063com,zuodao29,m.ks068.com,zzx2222,baoyu最新入口,www.5053dy.com,WWW.96533.COM,dayingjiaguojiyule,1598959982@qq.com,www . SB.SB 696. com,www.aa006.com,507789.com,www.112838.com,www.hg1763.com,www.wnsr5577.com,www.789728.com,wwweditofcom,ww3335544com,www.wn68.com,07521.com,www600w05com,wweviprandy5,594335967@qq.com,amdwc2,www.62155.com,www.61005.com,www.bet1871.com,www.99xam.com,www.118114.cn,yb4130.com,www.xpj48.com,jlzzjlzzyazhou,c1067613144,www.497201.com,www.70014.com,www.C3535.COM,www.5588ii,www.2059cc.com,peter98,www036cpcom,48887.com,www.176496.com,www.ylzz7.com,www.0854drf.com,37688b,www.741678.com,www.264072.com,wwwhe3456com,96516545@qq.com,361dy7,www.222066.com,778sun.com,www.y8622.com,2566o9com,www.154yu,www.963ii.com,long4784com,cp8365com,www.267678.com,www.rrr80.com,www.cs219.com,www.ll8303.com,www.165271.com,youandme,sts2221com,WWW.7JXF.COM,WWW.9784b.cem,sujue111,68789.cn,lmfs,cqwer150954,xpj7143.com,www.32188a.com,张家界市澧滨小学办学理念,wwwzxc663595859com,wwwibo266com,www.948225.com,guandaoyihuangxiaomanguanxiaoshuo,1770jj.com,tyc5185.com,www.lehu5288.com,708070.com,7878s.com,www.88btbt.com,www.vip.958300.com|

wwwhg929com,www.dy578.com,www.nn88ff.con,www.t088.com,www. qqbk58.com,wwwyhiiicom,83161.com,一录象片。 www.aodamy.com,www9896icom,sunzibingfatxtxiazai,www.pj1277.com,www.zn37.com,wokzyqwtalg,917777.com,www.s6666.net,www6783337com,www.bet252.com,qy194.com,wwwhg79com,www.030a.net,WWW.LUFAX.COM,wwwVIC004COM,www.y68tt.com,aqtyw10,wwwxpj9295com,wwwli044com,www.2455588.com,www.21mindmap.com,hgw168n.com,www.xa111.net,www.681150.com,WWW.HG5014.COM,www.pj000555.com,www.769yt.com,2jsdc. com,xffx0015,www3236588com,1716vip,tyc3913.com,61889,www.hg4251.com,www.ye7ye.com,www.55078.com,7mtiyu,www.yf77.com,yh60222com,xiaomayun,6676jj.com,xxddkk889,13322603229,wwwjc1631com,hg3376com,ggh523,hp00888.com,WWWCBCB078COM_WWW.CBCB078,COM,g00868.com,6chuan20zenmesuan,www.11108.com,wwwma1777com,www.74js.com,www.yuebet168.com,www.5866.com,812416com,nvmingxingzhenrenzuoyuantupian,00755.com,www59979com,ww898989,www.8843.co,h00088com,www.4057.com,wanghe888,7050o.com,wwwda388com,www.69977j.com,www.yb8777.com,www.751474.com,447888.com,WWW.05568.COM,zryl,www.hg982.com,www3009ycom,890679com,858666com,kk11kk.net,www.vns9608.com,0325138.com,rb805.com,6061vip,www.00660.com,897935com,jice43f3,wwwxiaoseniucom,www.58533.com,www.16008.com,2013966com,www.yl3888.com,www1888hk,www.56365bet.net,xpj0994.com,wwwhg720com,6688---55977cc/?Intr=58161848,www.668.cc,886974com,611aa.com,vw107.com,www.ag4773.com,7887999com,www.xpj8862.com,cqysyb00,tt00,2899msc.com,guoyunjian,www、XX280,www.www.branb988.com,WWW.92TU.COM,www.076898.com,djbetcom,www.929124.com,q892881306,www.ag5547.com,uuu558com,WWW.11922.NET,yabovip2955com,5011com,pgq123,www.0088hg0088.com,www03572004com,er882.com,www.6863280.com,jisu,q11223333,0006y,wwwcnpprcom,www.200hhcom.com,www.3603.com,hg123.com,www.85007.biz,yb9627.com,861961com,www.hg688.com,www.1194r.com,yb7589com,1972758274@qq.com,cp7s.com,d7817.com,948648088@qq.com,355366.com,www.bet6769.com,www.xinggei.cn,WWW.AG.4488734.COM,就去吻就去干,jlx123,ag5544com,www55659com,wwwdfh1006com,shuimu11,lao389.com,avmask进不去,wwwvns3000cc,www.55555102.com,958117.com,www.bbb501.com,www599600com,www.4975q.com,m.kf6816.com,848081com,www.hdg77.com,laonian.qingdaonews.com|

888888p.com,bf365.cc,hb110,www.hgw1199.com,0007j,980789.com,huabin9999,999565.me,,qqq2233,www90939com,cc5459,htk08com,www.353825.com,113000.com,11yue88,wanwz,WWW.MS666.COM,wwwbm8414com,sanguozhizhiliubeiyouziliufengtxtxiazai,www.209206.com,998996com,www876vcom,www6660yy,yobet234.com,www.m93488.com,www.jb069.com,aini123321,shenmadianyingyuanchaojiudianying,tshhswd520,www.50999q.com,jiangwei2013,|www.660306.com|www.js7,www.pj3882.com,www.cio.gov.cn,avtt2015tiantangwang,abctkcom,www222222nncom,ag82658.com,wwwgh0088com,WWW.BET8274.COM,WWW4402DDcom,www522msccom,3www...4568TTcom,www.999000.com,www64688com,www.2727365.com,sjyy0229,www.eee881.com,296381.com,www.jzd22.com,www99re7cnm最新网站,sezhongsedizhi,www11s8sme,www.eee421.com,制服丝袜qvod,www.266499.com,ks6222.vip,wwwa66yycom,wangyouzhijipinxingyunerxiaoshuo,www.00006004.com,6626ocm,www788ylccom,www.jjj88.info,www.hg112.com,621298COM,www.hg0031.com,20775454,www.312543.com,5780341,wwwqb05com,Y8Ya。com。,www.764688.com,3404e.cc,mg437722.com,www.51789.com,hg35com,www.3jc5.com,www.hk6668.con,www.www.vns00888.cc,aomenvn99com,bet6835com,wwwpj4567com,www.wp123321.com,wangyouzhijujishouxiaoshuo,akl6355,wwwsbd1010com,3133yh. com,29887z.com,liuwenyuan,www.38138.com,www.445544.com,WWWB444COM,ztlz,www.h959.com,www.864msc.com,www.226688a.net,jiangshan6.com,xpj4146com,zhifubao001,www.563483.com,www.hongtaozi.top/fo,www.yzxcyy.com,8366aa,www.611555.com,www22259333com,www.www1175x.com,www.249ss.com,4927b.com,www.0362.com,www.33288x.com,justfore@163.com,www.499sunbet.com,www95599cm,www.254489.com,xpj8445com,www.026685.com,hjwhjw1,www.811849.com,www.137suncity.com,www.s9797.som,1054cc,WWW.69911.COM,www070887com,chenglian,hdzgz,app3983.com,mg8206.com,山西工程技术学院贴吧,www.22666.net,okok699.com,adsdaa1,726408,cghhhj6699,63043156@qq.com,nh883com,yuhan0103,http://www.66epep.com,www.35BCT.COM,13626395241,www.8tubehd.com,www.nu666.com,huxurong,lhtrexa,www.1177dhy.com,WWW.WWW.83663.COM,wew242,11098.com,xin953.com,yabovip8553com,60335hai,2349zz,www.bet0792.com,900687,4v88.com,老湿机免费体检三分钟,2061237,jin2017jinshayule,www.xpj4021.com,WWW1515AVLU3COM_WWW.1515AVLU3,COM,mg5552.com,www.dhy3384.com,www.xiutv696.com,6648nn.com,1718199net,ttt664,dcy60,ttps,llwww|

以上会员名单排名不分前后