当前位置:首页 >> 数学 >>www.dodohh.com

wwwfengmi128com:【数学】2.4.2《平面向量数量积的坐标表示、模、夹角》-PPT精品文档_图文

www.160006.com hg55556.com www.zgcpw2.com vic2088.com 6325com www.seguigui00.com www.50596j.com

ks2503.vip www.55403l.com www.1469y.com www.35222.com winters wwwapwirecn www.333rv.com

2.4.2《平面向量数量积
的坐标表示、模、夹角》

二、新课学习
1、平面向量数量积的坐标表示

如图,i 是x轴上的单位向量, j 是y 轴上的单位向量,

?所以 由于 a?b? a ? b c os
i ? i ?1 . j ? j ? 1 .
i ? j ? j ? i ?0 .
b

y A(x ,y ) 1 1
j

B(x2,y2)

a

o i

x

下面研究怎样用

a 和 b 的坐标表示 a? b . 设两个非零向量 a =(x1,y1), b =(x2,y2),则

a?xi 1 ?y 1j
2

b ?x 2i ?y 2 j,
2

a?b?(xi x 1 ?y 1 j)?( 2i ?y 2 j) ?xx 1 2i ?xy 1 2i? j ?x 2yi 1 ? j ?yy 1 2j ?xx 1 2 ?yy 1 2

故两个向量的数量积等于它们对应 坐标的乘积的和。即 y A(x ,y )
1 1

a ?b ? x x y y . 1 2? 1 2

B(x2,y2)
b
j

a
i

o

x

根据平面向量数量积的坐标表示,向 量的数量积的运算可转化为向量的坐标运 算。

2、向量的模和两点间的距离公式
2

( 1 ) a ?a ? a或 a? a ?a ;

(1)向量的模 设a ? ( x, y ),则 a ? x ? y , 或 a ?
2 2 2 2 2

x ?y ;

(2)两点间的距离公式 设A(x1 , y1 )、B( x2 , y2 ), 则 AB ? (x1 ? x2 ) ? (y1 ? y2 )
2 2

驾考宝典网 jkbdw/ 驾考宝典 驾考宝典网 jkbdw/km1/ks/ 驾考宝典2019科目一 驾考宝典网 jkbdw/km4/ks/ 驾考宝典2019科目四 驾考宝典 jkbdw/kaoshi/km4/ 驾考宝典科目四 驾考宝典 jkbdw/kaoshi/km3/ 驾考宝典科目二 驾考宝典 jkbdw/kaoshi/km1/ 驾考宝典科目一 jkbdw/kaoshi/computer/ 驾考宝典2019电脑版 jkbdw/kaoshi/mobile/ 驾考宝典2019手机版 驾考宝典网 jkbdw/ 驾校宝典 驾照宝典 驾驶宝典

3、两向量垂直和平行的坐标表示 (1)垂直 a ? b ? a ? b ? 0

设 a? ( x ,y ), b?(x 则 1 1 2, y 2), a? b? x x 0 1 2 ?y 1y 2?
(2)平行 设 a? ( x ,y ), b?(x 则 1 1 2, y 2),

a // b? x x 0 1y 2? 2y 1?

4、两向量夹角公式的坐标运算
? 设 a 与 b 的夹角为 ?( 0? ?? ?180 ),

则 cos ??

a? b ab

设 a? ( x b? (x2, y2), 且 a 与 b 夹角为 ? , 1, y 1), (0 ?? ?180 )则 cos ??
? ? 2 1 2 1 2 2

x 1x 2 ?y 1y 2 x ?y ? x ?y
2 1 2 1 2 2 2 2 2 2

.

其中 x ? y ?0 , x ? y ?0.

三、基本技能的形成与巩固
例 1 (1) 已知 a ? ( ? 1 , 2 ?3 ), b ? ( 1 , 1 ), 求 a ?b , a ?b , a 与 b 的夹角 ? .

a?b? 1 ? 3 , a? b ?2 4?2 3?2 ( 1 ? 3 ) , a?b 1 ? ? ? cos ?? ? ,? 0? ??180 ,? ??60 . a? b 2

(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 ) ? a ?b
2 2 2 2

? a ? b ? 13 ? 20 ? ?7

练习:课本P1191、2、3.

例2 已知A(1,2),B(2,3),C(-2,5),
试判断?ABC的形状,并给出证明.

y

C(-2,5) 证明 : ? AB ? ( 2 ? 1 , 3 ? 2 ) ? ( 1 , 1 )
AC ? ( ? 2 ? 1 , 5 ? 2 ) ? ( ? 3 , 3 )
? AB ? AC ? 1 ? ( ? 3 ) ? 1 ? 3 ? 0

B(2,3) A(1,2)
0

? AB ?AC

x

? 三角形 ABC 是直角三角形 .

练习2:以原点和A(5,2)为两 个顶点作等腰直角三角形OAB, ?B=90?,求点B的坐标.
y 3 7 答案: B的坐标为( ,) B 2 2 7 3 或( , ? ) 2 2 O

A x

四、逆向及综合运用
例3 (1)已知 a =(4,3),向量 b 是 垂直于 a 的单位向量,求 b .

( 2 )已知 a ?10 , b ? ( 1 , 2 ) ,且 a // b ,求 a 的坐 .

3 ? ( 3 )已知 a ? ( 3 , 0 ), b ? ( k , 5 ) ,且 a 与 b 的夹角 , 4 求 k 的值 .
3 4 34 答案:( 1 ) b ? (, ?) 或 b ? ( ?, ). 5 5 55 ( 2 )( 2 , 22 )或( ?2 , ? 22 );( 3 ) k ? ? 5 .

提高练习
29 C (?3, ) BC ? AB ,则点 C 的坐标为 3

1 、已知 OA ? ( ? 3 , 1 ) , OB ? ( 0 , 5 ) ,且 AC // OB ,

2、已知A(1,2)、B(4、0)、C(8,6)、 D(5,8),则四边形ABCD的形状是矩形 .

b = (-3,2), a = (1,2), 若k a +2 b 与 2 a - 4 b 平行,则k = - 1 .
3、已知

小结

1、理解各公式的正向及逆向运用; 2、数量积的运算转化为向量的坐 标运算; 3、掌握平行、垂直、夹角及距离 公式,形成转化技能。
作业

课本P119A组5(1),9,10,11.


以下是今天幸运会员获奖名单

www.ag2673.com,WWW155BBCOM_WWW.155BB,COM,42450092.com,www.js333306.com,www.1314ye.com,ag6009.com,www55363com,yh88733,WWW.WW-63608.COM,wwwzb0212com,mail.10086.com,dwc979.com

www.qinglou555,yy4433,www5552007com,www.eee198.com,anqvye,743天天好彩免资料大全,www.pj86899.com,6664js.com,www.91002.com,www.www.slranzhi.comwww.slw1558.top,ag4627com,www.882008.com,www.799xj.com,WWW.059.COM,www365031com,sj32555,排列5平台网址=http:/,236hh.com,pss090611,wwwamyh309com,9127lb.com,lizysen,www.201228.com,www.1629df.com,hs19860626,a111819,www228448com,www.439999.com,www.333777e.com,22444.cn,www.80840.com,b66146,wwwjs666555co,www.wanli2200.com,shalong2012.com,55nsb.net,123455.me,www.y777c.com,www.czsjfloor.com,6659lb.com,763486457,www99523com,WWW.AK6996.COM,www.9229js.com,865003com,www.bxktv.com,wwwhk2222com,msx118,yinxiong,www.akak123.com,kaihusongmianfeitiyanjin,563414.com,hao01haose02在线,www.1515ee.com,lhc888.cn,www.fj.ct10000.com,www789818com,wapj.cc,cp5113com,www.bm8736.com,tyty8802,www.740033.com,www.www.198tlc.com,visa8899,www.943456.com,www.030552.com,www744567com,WWW.AM98882.COM,jgfgf852,www.vnsr002.com,wwwxpj0192com,dgaabbb,bbb456,www.59433.com,www.605858.com,525099.com,www.88850ww.com,www.967605.com,WWW1234SESECOM_WWW.1234SESE,COM,409497869@qq.com,ssnh86,www.478078.com,esd887,yingshidvd. com,www61479com,久久精品热2018,m.w88youde.com,www.9a334.com,www.749028.com,www.bm7672.com,ca0088.com,ks1114com,ks9951com,77suncitycc,haodiaoniu.com,wwwhe1582com,www.365.so,xiaoshuoxiazailuntan,cabc5678,tianjia,www.5553637.com,jangminjie@163.com,www.dg502.com,www612987com,76yhgb,rk1133com,wwwh888com,9090jj,www.690aa.cim,www.eee632.com,81189q7,www.70238.com,xlxx18,dujunwei,www.tm5518.com,WWW.G0042.COM,hongying8,www.wwww.com,zt1978,yh4895.com,wwwzx438com,www99000153com,yyy17.com,yobetyobet815.com,92xx中国,www.18zv.com,4848ss.com,www.m.rb130.com,oghh,ag8879comhuanyayule,www.bk2222.com,www.hg9587.com,www.2845509.com,www.hotspur88.com,9286d.com,www.ok49w.zg44.com,恋袜网站,WWWRE2255COM_WWW.RE2255,COM,www.tttxc.org,大鹏波多野结衣,www196196com,www.6696.net,www.61429.net,510101205@qq.com,www.42099.com,341022是哪里的身份证,www3344yacom,xpj3594com,banzhuchilaohudexiaoshuo,c3145487679,83639com,1429f1,wwwhb90779com,c700.com,dc1109com,www.51635.com,MANLIANYULECHENG,www81661144com,lj860213,wym2013,www68886com,www.98869.com,www.df888888.com,www.459999.com,www.www67558.com,WWW159YUCOM_WWW.159YU,COM,www.828990.com,yb7073com|

www,100,com,www.bm2770.com,www.335566.com,wwwjavcaocom,tyc882.com,www734466com,cqq79415256,660172com,wwwbet463com,855394com,www.pj3268.com,www.ggg138.com,www.86138.com,533dabao,148335.com,165msc.com,www.708876.com,toupaiguonayazhoucesuotoupai,www.heriqp.com,www.7777hd.com,www.xg0008.com,www.088303.com,60808.com,bjh56com,xiaowei970.com,wwwcp7000wcom,pp9856.com,www.wns7432.com,hghg83.com,wwwhk560com,14455gcom,wwwcpcp2222com,paipaigan,www.yls833.com,www.785678.com,2448xcom,18avmmcgcom,www.798999.com,6688---55977.cc,ag6066.com,www.mg8058.com,55papa新地址,www.22299.com,www.tongfa869.com,www.vip2966.com,wwwjs593099com,beiba673,www.111qqq.com,c782616639,s01858.com,www.3983112.com,bet6877.com,x9964x,xyyl008.co,yf022.com,13141314,64233.com,vip168 zxzx3,www.25149.com,wwwcs22888com,tyc2650.com,fuwen,www446668com,www.dhy0011.cc,wwwxhjc333com,77999.com,wwwi954954com,www.803765.com,gaohong,bet926.com,bldzy,js8848com,ag6106com,bobawang.com,wwwbchinanewscom,www.635141.com,www66am4422com,xrf3690,先锋资源2019最新进口,f111.com,www.381hk.com,1593s,662388.com,www.ag.kxmylc01.com,708365.com,www5050wwcom,www.66riri.29y2.com,zy139,hg1790.com,www.ggbb77.com,90916,www28166com,www4tube,bg947.com,www.8142111.com,wwwbtcr2com,wwwbw0808com,ks4972.vip,xpj6802.com,-WWW.4422N.COM-,15876685188,www.3344kt.com,sesepian,www.33382i.com,szepa11@yeah.net,www.vn365vip7.com,www554400com,www.x0000XDYW4.VIP,www.63584.com,www.xkd03.com,www.00332015.com,www.g8378.com,qingmengzhichuanqierxiaoshuo,www.6099977.com,www1194228com,www.7736o.com,z5632098,npnp33.com,www.525233,yb9497vip,a.bbkxw.info,js5573com,WWW,BBB397,cOm,www.8tubehd.com,www.xv333.com,xiaowei977.com,szs1122.com,www.yemalu.at,ty.dtj2544.com,ww2761,http://www.toyo-life.co.jp,6500r.cc,www.rf370.com,www.18555.com,WWW.DGDG8.COM,ag82136,huang8888,kdh970.pw,www.mgm1568.com,k7sha,cowgirl_730@163.com,sd2353@126.com,www.9349a.com,www.173158.com,www.888jbjb.com,WWW.HUI0008.COM,www.yun88org.com,10908.com,zbj0331,www.59bo.cc,898346com,uu2422,www.yl6670.com,wwwyhdc007com,792143420,775774,www.3049678.com,www.0760ks.com,vvvw224qq.3kp.in,www.5576com,www.98sihu.com,www.mimi.com,ag9467com,4797lb.com,ag1739com,wan4824.com,www.847624.com,shoucun10yuansongcaijinyulewang|

aac3266,lgy4977449,tyc2609.com,dfs60,www.0588.com,tycjt623.com,www.ooo48.com,799pao.com,wwwhwx444com,WWWagv1bet999net,www.yywxd.com,wof198018,www.qiyajt.com,ygyyh888,halima,591ysj.com,www.eez5.com,zl7994com,ben7788.com,zx8cv,www.bet5263.com,qyy5469com,bbin2018.com,www.035.com,36566com,WWW.6688DHYGW.COM,bbse18,238suncity.com,WWW.HG1144.COM,k10086,www.qylmm.com,www.36536504.com,www.88888111hk.com,www.budelu.com,yang613111,yy588.com,lyb8833,www.7889896.com,www.mgm5557.com,WWW01HZCV,999qe.com,www.451008.com,yb1584.com,www.hg1809.com,www.avtt2018v105.com,sejiujiuzuixinban,www. 304mu. com,www.ddm990.com,WWW.JS207.COM,www.180163.com,www.dmg773.com,fuyuan4scom,xin529.com,www.8858.com,lfjia,n8009.com,bet0630com,ckonka5987,www.vns2811.com,a2558288364,www.872444.com,www.953274.com,WWW.LH1388.COM,www.9588588.com,1660516616@qq.com,rf0788.com,www008798com,www38424pw,www.178nn,panhua71,6847.ag,8888sscom,www.3459c.com,www6funus,www.63365.com,www.hy865.com,www 150 com,91849.com,qweqee,6178com,www.xpj1106.com,www.www.5bbhh.com,www.uuuxxxx.com,songping222,wwwag33563377com,wwwhg1078com,ylg387.net,www.325,www.498666.com,www.37881.com,4060365com,www.261999.com,qifa836com,hg554.com,wwwxpj3net,wwwjs9244com,008vv.com,www.096622.com,www.tzlzcc.com,05789.com,WWWJAVBUSME_WWW.JAVBUS,ME,seqingwangzhan,www.238.com,js7164com,www.221735.com,huanghuang,hu6382,www.9942w,wwwxpg355com,www.xpj3746.com,jinbaowangzhuce,www52xieedcom,www.8015h.com,zl3225756700fuyg6467,aomenweilisiyulechengwangci,24866.com,yin102zxy,c1973yww,www.66cpcp.com,WWW.867765.COM,www.111841.com,lsls888.com,pwj06242612,www.am505.com,www.7pip.com,ks5399com,www.64649v.com,98798798dvgl,5599dhycom,pin3333.com,www.bwin778.com,www.33302m.com,www.qqihome.com,www.susu96.com,www.ma2666.com,yifaguoji.com,m.7819k.com,boluo11,www.fc1110.com,www4272com,tongfei,qwea789,zy.54114.com,EEWW99,www480829com,www.371111.com,wan0158.com,cmcxqx100,www.087159.com,Jockswwwwww京津冀,1167lb.com,niuyong,www.6he888.com,www.383077928@qq.com,ting123,www5599tkcom,www9599009com,www.26500.com,tyc2106.com,wwwyh3684com,www.ag.888bud.com,363005004q,www555xucom,pmz156,2839d.com,www.589r.com,wan3213.com,wxjnmyj.com|

yangzh,mu646359,www.099224.com,wwwsss1122com,8522.com,30033.com,www.111222i.com,www.zz22,wwwgg898com,23111.com,zhuyanan,bet704com,99163.com,www.220153.com,ok2021.com,160lao.com,1906622724@qq.com,3730-209,927dcom,www.42448.com,www.1991789.com,miya199.com,wangqing,namdalfhk.net,www.ag.3175522.com,caipiao99hcom,www.78854.com,www.16999961.com,www.77606333.com,570777.com,zyp11520,xpj0322.com,www.433456.com,www.js484848.com,www.413913.com,www.vns23488.com,www.123qqxx.com,hg3332.com,paiyqwdq,guo888888,wwwsemmcom,www.yh08699.com,wwwet3658com,wwwhg9640com,mg4793.vip,www.tyc937.com,www.KZCS5.COM,www8239com,747ysb.com,aiwin888447.com,13430394007,www.98849. COM,www.kz04.com,wwwvns88rcom,dⅴ568,C0m,KK028,C0mm,wwwyh356com,www.vns8731.com,qingqingcaozonghe,www.luoluo737.com,cvb999,www.650sihu.com,www.753suncity.com,www.bg852.com,www.ks5u.cn,18岁末年禁止观看免费网址,www.bmw1175.com,www2566com,qb744.com,3846q,www.ra82.com,www6119vcom,xuejunhan,wwwyz408com,ppvy121,www.8437666.com,zhongwenzimurenchengluanmazhongguo,www4107amcom,75msc.com,158757161,WWW.JS7002.COM,www389898wcom,www.eezvmle.com,www.111avtb.com,www.32367.com,48444,69598,so.yy111111.net,xiaoyu778,Liujing456L,youfa9932com,www.63349..com,www.bet411.com,lianggerenzuorenaidongtushipin,ybyl707.com,www.hui5511.com,lehu12,www3765jcom,sunji950121,bin904752521,rb444.com,www.7880123.com,xjfxjf,yb6495.com,192kkk.com,gg258,qiuzeilian7,www.jty749.com,xpj1608com,www.532010.com,lehaoyulepingtaizenyang,www.219hs.com,hg888788,se.78pao.com,WWW.188654.COM,zhangxiaobao,ag2613.win,www.09239.com,www.22886e.com,xpj5827com,www.12742t.com,3399h.com,wwwjs60099co,85595y.com,wwwkingbalynet,www.668155.com,www.30866.com,261suncity.com,0967bb,869049com,wwwk3355ecom,wwwc79xvip,wuxingyu,xdh88888.com,www.994201.com,www.777176.com,caiqiuyan,wwwzb769com,WWW895666COM,yb9514com,wjwwjw,wwwzfw998com,www.27173.com,123111com,wwwcdgdcedu,ag7328vip,914lao.com,www38gg,http://片在线www.56.com xn--www-lp6eu78dcybvy8awzw.56.com yigou110.c,WWW.47769.COM,ky1006,www.19zt.net,872034com,jisu6666.com,www658899com,ag.wxc6667.com,1300535795@qq.com,853340com,www.9189.com,www.s8s103.me,bian888,nianqingdemuqin2tufeiguankan,www.596mk.con,www00749com,www.mk828.com,www.js4528.com,www.zr2266.com,www.cs2088.com,dfs8123|

以上会员名单排名不分前后