zw963:2019年2.4.2平面向量数量积的坐标表示、模、夹角(1)精品教育.ppt_图文

3537.ag www.ttdxj.com 2299k.com hyjlj520 www573059com www.821206.com wwwnbg4com

fffhed00 www.xin59.com www.dckgx.com www.lgtwh.com yhw0077.com www.87655.com www.007ee.com

1、 a ? b ?| a || b | cos?

2设 (、1)a?a数?、?量b?b积是 ? ?的非性零a? 质向 ? b?:量? 0

(2)当a?与b?同向时,

a?

?

? b

?

a?

? b

当a?与b?反向时, a?

? ?b

?

?

a?

? b

特别地,a ? a ? a 2 或 a ? a ? a ? a 2

(3) a ? b ? a b

一、平面向量数量积的坐标表示:

i ? i ?1

y

j ? j ?1

b

a

i ? j ?0

j

oi

x

设:a ? (x1, y1),b ? (x2, y2)

则:a ? x1i ? y1 j, b ? x2i ? y2 j

一、平面向量数量积的坐标表示:

? ? a ? ? x1, y1 ? ,b ? ? x2 , y2 ? a ? 0,b ? 0

a ? x1i ? y1 j, b ? x2i ? y2 j

?a ?b ? (x1i ? y1 j)(x2i ? y2 j)

2

2

? x1x2i ? x1y2i ? j ? x2 y1i ? j ? y1y2 j

2

2

i ? 1, i ? j ? 0, j ? 1

?a ?b ? x1x2 ? y1y2

二、向量的模和两点间距离公式:
?1?向量的模(长度公式):设a ? (x, y),
则 ? a ?2 ? a ? a ? x2 ? y2 , 或 ? a ?? x2 ? y2
?2?设A? x1, y1?、B?x2, y2 ?, 则AB ? ? x2 ? x1, y2 ? y1 ?
? AB ?? ? x2 ? x1 ?2 ? ? y2 ? y1 ?2

三、向量夹角公式的坐标表示:
设a ? ?x1, y1 ?,b ? ?x2 , y2 ?, a与b夹角为?,?0 ? ? ? ? ?
cos? ? a ? b ? x1x2 ? y1 y2
| a || b | x12 ? y12 . x22 ? y22

例1:?1?已知a ? (3, ?1),b ? (1, ?2),
求a ?b,| a | ? | b |,a与b的夹角?.
解? a ?b ? x1x2 ? y1y2 ? 5
| a | ? | b |? x12 ? y12 . x22 ? y22 ? 5 2
cos? ? a ?b ? 5 ? 2
| a || b | 5 2 2
?? ? ?
4

?2? 已知a ? ?2,3?,b ? ??2, 4?,
则?a ?b???a ?b? ? .

法一:a ? b ? (0, 7), a ? b ? (4, ?1) ?(a ? b)(? a ? b)? 0? 4 ? 7 ? (?1) ? ?7.

法二:(a

?

b)(? a

?

b)?

2
a

?

2
b

?| a |2 ? | b |2 ? 13 ? 20 ? ?7

四、向量垂直和平行的坐标表示:
a ? ? x1, y1 ? ,b ? ? x2, y2 ?(a ? 0,b ? 0)
(1)垂直: a ? b ? a ?b ? 0
? x1x2 ? y1 y2 ? 0
(2)平行: a / /b ? b ? ?a
? x1 y2 ? x2 y1

例2:已知A(1, 2),B(2, 3),C(?2, 5), 求证:△ABC是直角三角形
证明: ? AB ? ?1,1? AC ? ??3,3? BC ? ?? 4,2?
? AB ? AC ? ?3 ? 3 ? 0
即AB⊥AC, △ABC是直角三角形.
想一想: 还有其他解法吗?
AB ? 2, AC ? 3 2, BC ? 2 5

例3:已知a ? (4,3),求与a垂直的单位向量b

解:设所求向量为(x, y), 则

?4x ? 3y ? 0

? ?

x2

?

y2

?1

?

? ? ? ?

yx???534或????xy???453

? 5? 5

?b ? (3 ,? 4)或b ? (? 3 , 4)

55

55

例4:已知a =(1, 0),b =(2, 1),当k为何实数 时,向量k a- b与 a+3b(1)平行;(2)垂直
解:k a- b =(k-2, -1) a +3 b=(7, 3)
(1)由向量平行条件得3(k-2)=-7 所以k= ? 1 3
(2)由向量垂直条件得7(k-2)-3=0 所以k= 17
7

练习
B

C

D

23 3

1

m=-2
?
6

A

小结
1.a ?b ? x1x2 ? y1y2 2. AB ? ? x2 ? x1 ?2 ? ? y2 ? y1 ?2
3.a ? b ? x1x2 ? y1y2 ? 0
4.a / /b ? x1y2 ? x2 y1 5.cos? ? x1x2 ? y1y2
x12 ? y12 . x22 ? y22


以下是今天幸运会员获奖名单

tyc6579.com,www.6688e,www610180com,67816.com,8025.com,58tongle11.88,303202com,www.92mmmm.com,3333lbcom,www.blh1133.com,820178com,www.70422.com

www.9988ny.com,guangguang66,baoyutv入口,tyc8407.com,laibafile.cn,cp5306com,www.170641.com,www2865899com,wwwbm3708com,xed01.com,www.shenbo90.com,julongsheyule,qp999.com,www.6613.com,www.90684.com,wwwhg9601com,666sss,www.mgm1898.com,8090lu.com,www.741777.com,www.87123.com,ww13255com,www.637499.com,www.3190ee.com,mm19.net,asdadas2,yd6889.com,m.xeacg.net/shaonv/list_2_,yt0108,www.ckf580.com,www.v68.com,jp1902.net,zz777,a123110,26k66.com,www.k4488.com,a891199,www.47301.com,www.437dh.com,www897728com,zm1890205298,wan4044.com,suncity32.com,www.ryf88.com,www.yl863.com,www.marksix.mixa.cc,yabet4565com,www.6658n.com,855169com,yb0195.com,19883539141,www27877gcom,35579.com,www.xpj4735.com,WWW.115MSC.COM,www.uc3999.com,hg5000x,9885s.con,sbd0004.net,cq.189.cn,https://m.sogou.com/web/sea,5869lb.com,8rrr,xpj3202.com,www.28299.com,wwwkxmav18com,www.576:com,977755.com,zl4120com,www.6137f.com,www.tt833.com,zuoaizishitujie,2544m85,wwwaobo100com,:https://www.fj111.xyz/?tg=1,wan3710.com,chiesefemdom视频vip,www6576888com,cai.yj666.xyz,www.pj88pp.com,www.jj4283.com,1750888888.com,tyc4471.com,hg836bb.com,www.2355.com,wwwsb9566com,yingliechuantxtxiazai,w479518509,www760633com,www.2488,zs442.com,www.1532888.com,www.072106.com,wenzi,wwwqpl02com,120,yb1062.com,2605539vip,hg7975com,www.149361.com,www-202597.com,www.6541.com,wwwll2848com,www.5009077.com,www.868615.com,wwwbm6668com,hpj582,lisir520,yb4928vip,agent.03uu55.com,www.772954.com,xpj0219.com,498765.com,www.s8.com,www6227001com,www. avtb123. com,www.8886.hk,619938.com,h tt p: //www. by 1275.com /?u,wwwhptx3com,www.2767z.com,zs350.com,WWW.24677.COM,dariben99,www.9980j.com,@$SGS#@sogousearch%3A%2F%2FopenUr,WWW.38818.NET,nnuu22,sg1.sznkbz.com/wenda2,www.1233288.com,wwwvip00217com,www188266com,zuidazuqiu,www.589tpve.com,WWW.BOCAI4066.COM,644114,www.2230775.com,ag6797com,2949.net,www.288566.com,wwwppyppcom,uy666.com,wwwcs3300com,www28999com,zhaji035,www.diqises.com,www.olex2211.com,www.i06617.com,m. sun369. com,www78122com,hg97net,www.kpindao9.com,tv238.com,1.11222E+11,abo4374,www.6666.comm,www.027hh.com,www.864277.com,wwwam05005com,qinqin890503,www.387.com,812167com,yb1033.com,xpj8917com,wwwwwwra63com,xiangyuchuan,234av,www.02466.com|

998996.com,www.jsp02.com,www.1178h.com,xpj7002.com,65322,www.hg874.com,3333pp.com,www.xg536.com,www.sb7792.com,ag8300com,www.49123.com,Dosjduo7649,WWW.AAA333.NET,www.778999.com,0088333.com,lilingui,www.229.com,www333568com,WWW.4982.COM,www1590cccom,wwwjuqengcom,yf111.com,www.59911b.com,www.1492.com,www.m0099.com,www.387277.com,www.kxcp85.com,hg7bet.net,dabao522,www.789tk.com,www.1111.com,shoujikanpianyazhourihan,www.ee165.com,www.33999a.com,www.401313.com,bet36557365v.net,www.dbyyh.com,s8sp com,biz.0437.com,bomao525.com,bg612.com,woaiwodejian,296237.com,7553kcom,44kcd.com,wwwpj44555com,www927444.com,WWW.Y7749.COM,ag87009.com,galgame.net,ag80923.com,66693.com,vns6652com,www.h5fr.com,www.xpj26789.com,hg7754.com,nkrwxg.com,k0077com,www.3196666.com,www.wh339.com,帐号,2058719061@qq.com,m.mg520ss.com,www501msccom,qq4167,WWW.TT3377.COM,qq729398549,www.hbzhan.cn,www.cr960.com,www380800com,www.6635msc.com,ffggh,www.775775.cc,sobkk,vns0377.com,3917.win,WWW.G3710.COM,wwwbm4321com,www.k66.com,www.y3338.com,kb933.com,www.097779b.com,www.006678.com,www.bwin607.com,7660582,853suncity.com,ks668.com,yabovip7797com,www.055118.com,liu2008,www6608xcom,www.xpjuc222.com,www.dn588.com,feng12240898@163.com,00899h.com,zxj88888,www.feferi.com,666ysb.com,js0507com,long7757com,www77508003com,xxx777888,palwan,757855831,www3983115com,ag4393.win,pg124.com,51133gggcom,ab1788.com,wwwp5895com,494cc,www.123.sogou.com,视频亚洲图片小说,pangfei365,avwangzhanm,www.952ii.com,kb4491com,baidu.co,wwwhcmobi975555com,www.bm4913.com,www.3044343.com,www.dwc771.com,856cc,3434fff,51999a.com,ad.tl666666.com,minikkd12,aa777,wwwecp6677com,hg7757com,www.sperge.com,www2165com,wwwgg1155com,www.896234.com,czyy75131,wwwduchuan4com,xed02com,www.vip.hg929.org,WWW.8730M.COM,wwwt365777com,ag5752vip,China free viedo,jiangjiang@gmail.com,ag8927com,zunyi853.com,www.5917.info,www.ok24148.com,www.sun699.com,yb6650com,www.0814hu.xom,wwwms4949com,a6858447,www.666308a.com,www.038ee,www.xqxq,www77159com,www.44438.com,WWW.HG0580.COM,www.gntomato.cn,www.7jsjs.com,www.j70888.com,811102.com,www.163480.com,www.697799a.com,mgdianziyouxiwangzhan,www.xpj8642.com,www.5qqcc.com,www.pj33305.com|

415533.com,www.hg8853.com,692123.com,831780com,xpj8320.com,www.e33303.com,www.tb6611.com,ab1428.com,www.hbs419.com,www.665888005.com,www.lv9888.com,873340com,wwwvns18333com,www.44413.ocm,883377路com,ks0344com,3344jl.com,wwwcp471com,www.777202.com,wwwmg8453com,wwwbet9091com,(pornhub)https://cn.p,www.4hu5.com,www.amxj2277.com,314866.com,qyy2781com,www.90125.com,www.hhh895.com,1488wa.com,0275bet,欧美freeones,aass2222,www.a25v.com,asdf785,6067.com,www.yh8085.com,www.dzc8.club,cqingzhi,971hs.cim,www.1992885.com,cslong,sb8811com,18suimonianjinzhiruanjian,wwwts298com,m.6k66.vip,874135com,18禁短视频app,WWWOOOO555COM_WWW.OOOO555,COM,ask3355com,babadehao,wwwpy52099com,yl82688,83210,011799com,bet365334365.com,hik3333,www778778778com,wan0638.com,www.79198a.com,rb338,www.haokanzyz.com,hh22me免费看片入口,www.jnh992.com,www.pj646.com,www.00036.com,www.54143366.com,www.hztzfzjt.com,wwwcr678com,5296686.com,eng.spdb.com.cn,www.8009966.com,3p22.com,vv8999.com,ww.038cp.com,282991903,www.16295544.com,www.0965.com,www.03.bet,m. abtt777.com,www.zhobo8.com,wwwahgcjscom,www455488com,6594com,kanku影院,fhgj02.net,like6711,www.427222.com,m.12bblu. com,9820.com,69955.com,www85116666com,wwwqy666com,www99665004com,wwwysb66com,5566新永久域名发布器,www555558com,2566m5,www.wns9584.com,www.4237rr.com,www.14571.com,www.456123.com,yabo098.com,www.m8789.cc,www. 278YU. COM,sd2341,sbd9966.com,WWW.BET36577.COM,8877342.com,kongming,wwwxg6hcom,long540.com,http://www.234888.site/,0304lb.com,beker2012,am66xyz在线,www. av377.com,www.76789.com,www8800883com,wwwp7720net,www.8096yy.com,jing7555.com,www.bwin299.com,ymkj520,www.367558.com,ny686com,0255022.com,wwwvns70333com,cp0634com,l5555.com,liuna11,www.9992184.com,天天鲁在视频在线观看,久久这里只精品国产99re66,yb0007,bbbb8info,huangma34.com,www.xpj2248.com,www.wxc5599.com,www.www64644.com,ggh156,www.3652654.com,wwwdedepacom,803664com,cao0019.com,vv31365.com,lintaoa,wb4401com,lufu,894946com,华为棋牌 www.weimanzs.,www.30344..c,www8881171com,www.66023.com,www.65565533.com,556636.com,sd6255,un2200,mg1073.vip,www.3232b.com,wwwii402com,www.22geg. com,www.ng5.org,www.655333.com,2066.com,www.youi.122.com,xx123321,q276584304,89922com|

wzln,WWW.DSN6.COM,www.567dog.com,www.xpj7574.com,cjamyaaa@hotmail.com,youfa6139com,fun18,www.211vv.com,13680.net,886319com,wwwsjc003com,wwwshenhuayulechengcom,www.2208.com,www.3132017.com,chenyao1,www66185com,yecaifu12081,www.2824k.net,am66xyz在线,www.cpta.com.cn,www.sb9952.com,www.99NN7.com,1515.com,www.393713.com,www.1111gf.com,欧美一级观看 www.f3xr.com,lianyong,dhy669999com,qy3529vip,www.3813847.com,www.636929.com,www.hg00200.com,39333.com,www.19523.cn,voicehentai,yf2666.com,WWW.142543.COM,www.28365.mobi,m.623b66.com,www.2245aa.com,www.1382.cc,a8254,wwwdwns6868info,www.cbkccc.com,a673382,www.jch688.com,lh4122.com,714567.com,www.36161.com,sl88h.com,www.henhenlu.com,www.aavbook.fun/m/,www.lupodi.com,rb0024.com,vns0411com,agent.152665.com,www.984947.com,wwwma0044com,www.jd6333.com,www.se0648com,www11009com,c62409891,gg362,www.98786.com,www.semange.com,wwwc5856com,js2508com,lishui.98066.com,wwwjs76666com,491666.C0m,5627v,bet3652835kcom,837657com,www3045dddcom,wwwcaitou02com,yuexingxixiaoshuo,www026099com,czsp22.com.,xpj6824.com,625103.com,www.9998998.com,wxc961.com,www.22279.com,818181cc,xujiaxing,yudanzuibang,flp88,WWW.HG2652.COM,jiujiuseyouyouwangyingyinxianfeng,www.ive5.spbo1.com,www.hg0020.com,guiwaipozhixiangcunyouguitxtxiazai,nanrendi4se,jinshp31.com,https ://www.288yu.com,WWW.HG6734.COM,WWW.PJ555999.COM,wwwam9111com,www.ks279.com,yunjian12,woaini@163.net,www.915604.com,www.883737.com,www.730msc.com,wwwcaipiao016com,tcp027.cc,www.99181b.com,sexlnsex.board,www.20266.com,hhh138.com,www.3k3kk.com,x78pp,xyjingyu,wwwpj30789com,5hg1088com,www.win8312.com,www.1125999.com,www.flgj444.net,www.bw9998.com,www.649111.com,ct6kgu76nmv7,dy11.com,wwwbet584com,WWW0n12345nm0,www.yh467.com,a123321,www.jiv66.com,R9854D,848189168,3658bfvip88com,7893w71.com,yobet929.com,562030com,www.56700.com,www.620425.com,bte999com,cweng,15278888600,www.k775.com,guanggendianyingyuanyy11111,www.6969.com,www000322com,www. 96krb.com,hg7626.com,秋霞手机在线新版入口,hg6279.com,72a6ii88r9,youfa6425com,5451lb.com,lanlifei,WWW.8281.COM,yb5742.com,www.006118.com,www.hg5737.com,baomayouxidengluwangzhi,www.denexport.cn,ag88844.com,2.1449www.u8see.com,42450076,www.222e1.com,万维网MAHUAa音的唱,www.943bbin.com,WWW.WWW.BET9422.COM,xpj7071com,WWW.9M138.COM,gengjia,www.255y.com,bbs.cqlp.com|

以上会员名单排名不分前后

相关文档

2019年242平面向量数量积的坐标表示、模、夹角 (2).ppt
2019第1部分 第二章 § 6 平面向量数量积的坐标表示教育精品.ppt
2019第1部分 第2章 2.4 第二课时 平面向量数量积的坐标表示教育精品.ppt
2019年2.4.1平面向量的数量积精品教育.ppt
2019年2.4.1平面向量数量积精品教育.ppt
2019年2.4.1平面向量数量积的物理背景及其含义(1)精品教育.ppt
2019年平面向量数量积 (2)精品教育.ppt
2019年2.4.1_平面向量的数量积的物理背景及其含义精品教育.ppt
2019年2.4.1平面向量数量积的物理背景及其含义精品教育.ppt
学霸百科