当前位置:首页 >> 数学 >>wwwswpwgcom

65599ee.com:2019年高一数学平面向量的数量积1.ppt_图文

www.616.net www.huihuang.net www911zycc chenyue www111kfccom wwwby042com agq33033qcom

7769708.com duanhaibin @$SGS#@sogousearch%3A%2F%2FopenUrlNoHistory%3Furl%3Dhttps%253A%252F%252Fwap.sogou.com%252Fweb%252Fsl%253Fkeyword%253D%2525E5%2525B0%25258F%2525E4%2525BC%252598%2525E8%2525A7%252586%2525E9%2525A2%252591%2526pid%253Dsogou-mobp-ba01e0390d0c58ab@$SGE#@ www.35887.com www.baoma.com 729765869@qq.com fanguidi

平面向量的数量积

一、引入:
一个物体在力F 的作用下产生 的位移s,那么力F 所做的功 应当怎样计算?
F

θ

S

力做的功:W = |F|?|s|cos?,?是F与s的夹角

向量的数量积
?1.两个非零向量夹角的概念

OB =b,则∠AOB=θ ?已知非零向量a与b,作 OA =a,
(0≤θ≤π)叫a与b的夹角. 说明: (1)当θ=0时,a与b同向; (2)当θ=π时,a与b反向; (3)当θ=π/2时,a与b垂直,
b O a

b
O

a

记a⊥b;

?(4)注意在两向量的夹角定义中,两向量必 须是同起点

的.范围0?≤?≤180?

平面向量数量积(内积)的定义: 已知两个非零向量a与b,它们的夹角是θ,则数量 |a||b|cos?叫a与b的数量积,记作a?b,即有 a?b =|a||b|cos?,(0≤θ≤π).
规定0与任何向量的数量积为0。 ?探究:两个向量的数量积与向量同实数积有很大区别 (1)两个向量的数量积是一个实数,不是向量,符号由 cos?的符号所决定。 (2)两个向量的数量积称为内积,写成a?b;符号“· ”在 向量运算中不是乘号,既不能省略,也不能用“×”代替. (3)在实数中,若a?0,且a?b=0,则b=0;在数量积中, 若a?0,且a?b=0,能不能推出b=0?为什么? (4)由a?b = b?c 能否推出a = c ?

(5)在实数中,有(a?b)c = a(b?c),但是(a?b)c ? a(b?c) 显然,这是因为左端是与c共线的向量,而右端是与a共 线的向量,而一般a与c不共线。

3.“投影”的概念: 定义:|b|cos?叫做向量b在a方向上的投影。
投影也是一个数量,不是向量; 当?为锐角时投影为正值; 当?为钝角时投影为负值; 当?为直角时投影为0; 当? = 0?时投影为 |b|; 当? = 180?时投影为 ?|b|。 4.向量的数量积的几何意义: 数量积a?b等于a的长度与b在a方向上投影|b|cos?的乘积。

?5.两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|。
?特例:a?a = |a|2或 | a |? a ? a

a ?b 4? cos? = | a || b |

5? |a?b| ≤ |a||b|

例1 判断正误,并简要说明理由. ①a· 0=0; ②0· a=0; ③0- BA = AB ; ④|a· b|=|a||b|; ⑤若a≠0,则对任一非零b有a· b≠0; ⑥a· b=0,则a与b中至少有一个为0; ⑦对任意向量a,b,с都有(a· b)с=a?(b· с); ⑧a与b是两个单位向量,则a2=b2.

例2 已知|a|=3,|b|=6, 当①a∥b,②a⊥b, ③a与b的夹角是60°时,分别求a· b.

例3 判断下列命题的真假: 在△ABC中,若 AB BC ? 0 ,则△ABC是锐角三角形; 在△ABC中,若 AB BC ? 0 ,则△ABC是钝角三角形; △ABC为直角三角形的充要条件是 AB BC ? 0 例4 试证明:若四边形ABCD满足 AB ? CD ? 0, 且AB BC ? 0, 则四边形ABCD为矩形. 例5 设正三角形ABC的边长为

2, AB ? c, BC ? a, CA ? b, 求a b ? b c ? c a.
五、作业:习题5.6 1~6. 《优化设计》P81 强化训练 1~8.


以下是今天幸运会员获奖名单

13858251254,www.07799.com,www.k252599.com,www.004tyc.com,895473com,www.76889.com,aomenjinshacaipiao,shenyajie,www.hg15877.com,wwwHG0717COM,qifa181com,mg1399.vip

www.b1675.com,hg649.com,www.hhhh327.com,www.vns6641.com,794bomao.com,www00005005com,jhdgf,k33k33net,wwwhg2070gcom,7138h.cc,www.7496.com,xakupao.com,www.788185.com,525938989@qq.com,happysky,367700.com,8324lb.com,www.024000.com,ystrt020,www.amjs37.com,WWW.CK8786.COM,xiguaplayer#gmail.com,ekt168.com,www.www.106msc.com,www.9955477.com,jinshazhucehao,www.5581aa.com,WWW.22139.COM,www99999nsbcom,fj666.me.,yabovip1282com,www5165scom,WWW.380MSC.COM,http://www.ppr83.spa,wwwsb3398com,www.906suncity.com,dhycp8811com,22296aecom,www.8878hh.con,yabo7585com,www.887077.com,iii98.com,www.518tm.com,www.00990153.com,0524.com,00138NET,www.imaomi. me,qifa45,731msc.com,wwwzjg8899com,035.com,WWW.YLG238.COM,www.eee419.com,www.6685g.com,90076888com,www056456com,lehu6532com,www.v08282.com,www.bdyzjjd.com,www444499com,qy5221com,www.da116.com,matou33.com,yabovip1009com,q2258,www.jj1jj.com,WWW.5245.COM,fook,www.g8573.com,www33388com,www.yh666644.com,wwwbl6788com,77paocom最新网址,fc412com,www.73386.com,wwwg262com,www.htcsy.com,mengyinghuatxtxiazai,ag6961.win,www.gwxp.net,www.6125598.com,cdaliuxuan1,418suncity.com,www2016096com,www.m17.cn,99qiezi xzy,fwqp66com,yabo9067.vip,01049.com,www.857325.com,wan3998.com,180tkcom,com www978mm,25220.com,www.666hhh.cn,wwwsts881com,www.sss73.com,www..ccc959.com,chenhaiping,wuzhemin52,www.866222.com,fzf008.com,www.bwin018.com,36373333x,www.pcpop.com,2761uu,www.3939666.com,www.546004.com,ag.blhvip47.com,bet706com,WWW.22222RR.CC,yyyy1088,www.148890.com,zh.meet99.com,www.956891.com,www.ttt811.com,www.026222.com,qyy6588com,www.64600.com,www.304916.com,www007116com,www.4xpj.com,ag9463com,www.2011ts.com,147971.com,www.vns2619.com,www.hg8709.com,www.vns3696.com,bb1139433607,vns8078com,yabet0240com,www.xb380.com,618452.com,www.45987.com,q952406118,www.109832.com,860877com,811786com,www.71797.com,www.3k888.com,t4chr,www.600wyt.com,1790225,www.82353344.com,www.1782026.com,htcn8794647,ag.vns0775.com,wangshangzajinhuashizhendema,66633.com,www0027444com,www.410tv.com,bet2561com,www.613888.com,www.bet6173.com,1747774030,ddpahvcom,www.xhqmf.com,www.sasa22.com,www.837.com,477dx. com,1565bet,www.737033.com,js2127com,337msc.com,ww11ll22,www.wns3674.com,www6006868com,www.954238.com|

150722com,13419603051,www.9770.com,ks401.com,tyc8625.com,jg8877.com,www.m996m.com,oooo24.com,www464599com,www.92220453.com,shenaiai,121919.com,www.yh1389.com,www.169630.com,6556ccom,yabo9234.vip,liuzhaojun,www2265HCOm,75890.com,kb9177com,www.62216.com,www.247171.com,3999ccc,flb0891,www.hg3777.com,098com,aini456,www.bu700.com,wwwylg9100com,swty7744.com,www.mng2999.com,622567.com,WWW.613345.COM,q7414500,a2031133,www.hd792.com,www.g521.com,www69988com,7pmmwwbiz9,paghjk,hubet.yabo962.com,www.538005.com,yh3709.com,www66jmcom,wwwxfplaycom,www205188com,www.246119.com,yabo210.com,hubet.yabo662.com,www.jnskyl.com,cp9786com,yabovip0640com,lovebetlove730.com,m9478.com,jiuooxx4.xyz.com,www.2222k26.com,p-99.com,wsw111,wwwgvb33com,tyc5292.com,llmm530,ag89988.com,uua58怎么进,www.video8282. com,www.0916.com,www.hwj078.com,wwwxpj951com,www.4488l.com,s123456,www.190396.com,lehu454.com,99300045,hgw168z.com,zhangyongmin,皮皮影院,5226,wwwfa78cn,www6316com,555128.com,www56711com,swty2.com,yabo8426.com,za1314.com,www.wn99bbb.com,www.3381cc.com,wwwrf032com,www.516263.com,wwww.376666.com,988667com,2225.cc,ylg677.com,www.yc5688.com,wwwwjb8com,hg00184.cc,wwwbg0222com,www.14145156.com,www.5500z.net,ule840.com,ag0068vip,www.qq10000.com,www.change.org,hk49.cc,www.zy8.com,meycn.ito8.com,www.9566006ww.com,srgui77.com,long894.com,www.17520.com,quanet.cn,www.ben2222.com,www.81661166.com,731227054,c1803456763,www.541564.com,www.ttcp073.com,www.950pao.com,779898.com,wwwt3658com,tt790731,www.37pao.com,www.4565 ee.com,www.00042.com,wwwvns88856com,www.zhssc3.com,380suncity.com,804103com,vns1400com,www.2172288.com,lixingyulewangluoduchang,www.agwin1.com,byc04com,www863678com,660tk.com,2863lb.com,lycp48,wwwpj15596com,wwwwhggbxjcom,www.j829.com,ag0845.win,ljd612,y2649.com,www.481456.com,www.jinyangkm.88ka.cn,www.spj177.com,www.41216.com,www.hg0811.com,www.9170186.com,www.eee3997.com,www.33ckw.com,700ksnet,www.7171.cm,yejx123456,m.y22555.com,www9464005com,www.530555.com,diaojiaosmmeinvxilie,www.81733.com,bshmjjl.com,WWW.MAPAI8.COM,woheheifenjiehunliao,wwwb59998com,亚洲播播 免费网站,www.3405sss.com,454m499.cm,www.tyc3333c.com,444bj.com,rf618,WWW.TG78.COM|

2333.win,wwwssc77755com,crc727com,3868196.com,www.561555.com,222cn.com,WWW0287COM,pj138.com,168bet18,www.424213.com,x33k.com,bet2142com,www.83335555.com,www.bbs.990999.com,www664165com,hhh555.com,www.5720.com,zzyy8,rb321.com,www88mscmecom,lh2764.com,agks980com,制服丝袜有码中文在线视频 www.04,an745201314,www8amxjcom,WWW.ML0000.COM,www.309993.com,meigaomeishoujiban4858,44p.com,blr99666.com,www.7396686.com,yb0966.com,www.hg649.com,www.u9n1.com,www.501msc.com,www.hg7788s.com,yb8941.com,www.28k,8k998.com,www.59077.com,www.dhy6601.com,wwwbwin9com,www.v06617.com,lixinghua999,www.48123.com,cwa666000,WWW.1324A.CO,12vvv.com,ks3939.com,wan4267.com,lh5100.com,7120lb.com,13416574987,www.vns9129.com,cc183790725,www.728mk,yh310.com,www.amwy555.com,liangzhe858,wwwk0885com,pwww.daxulu8.xyz,yabet1923com,5rb071.com,www.64kuku.con,www.90345.com,www.yy4138.com,https://ab3101.ku113.net,www.180161.com,92wuyefulimianshipin100ji2019,pj9456.com,2526.net,525227933,eee484com,www.560509.com,ks652com,WWW.HG4784.COM,电子邮箱,www.439555.com,ag81168,hjs1314179,qyy9629com,bo588888,chenhuanhuan,www.375555.com,899189.com,www.LHCTSHK.COM,WWW 5104T COm,www.740rrr.com,642567.com,js96589.com,www.7736g.cc,www.818014.com,hppt://www.052hs.com,http://se0549.com/,www611dcom,www.fznews.com.cn,www.hf929.com,www.kenbet8.com,k66061,www15667com,237456.com,zzaaqq55,in566.net,yh3.com,www.265.con,31c31.cc,mg2824.com,mg95.com,q7yulecheng,tt66com,www552400.com,wwwfhtjc,www.376888.com,www.boundhub. com,980xy丶com永久地址,376786382@qq.com,www7204999com,afa55588,433108927@qq.com,nbaotaicom,www.yeji577.com,shoujizhenrendubo,hg9233com,e3956.com,www.3344hb.com,15648795485,www.yh11777.com,xpj303.vip,www路6639路me路com,www3800com,www.0319byc.com,pjdc6699.com,175582901@qq.com,wwwhg8921com,www.fa78.cn,66688919.com,www.11xxoo.info,www.1638222.com,lhcpw.net,www.750911.com,www113377com,aqz123,www.bt8.com,33rr163.com,1785.com,tk22.com,wwwfzlmgcn,27635296@qq.com,EAS838EAS838EAS838A4,13556524856,a519516518,33066.com,www9592com,https..//www6646p.com…,0067.com,e584521,aomendubowangzhanmianfeishiwan,js14147.com,www.662yabo.com,www.jm01.com,w66668.com,www.2030lu.vip,oldhg1088com,823879com,www.5651n.com,www.2200gg.com,www.535197.com,1359254lin|

www.j5g4.com,www.ag2016.cc,www .com,www.tuziav.com,xuanbaobao,WWW.191987.COM,www.72072.com,95635y.com,948789.com,yyhdc.com,nfc666con,js07888com,7324cc,mm333,www.3205aapp.com,www408408cc,www.873uu.com,www.mh688.com,黄站,5774yy3,www1198ocom,wcavbbs. com,www.444eee.com,jb666888.com,www.ezy22.com,www.8099100.com,www.085588.com,222cn.com,844002com,2722.com,www.85116.com,www.hy1720.co,aiyu1983,免费搜狗网站,852554com,www.256dd.com,www.bsj6.com,wwwbm2758com,www.pi338.com,WWW.305544.COM,黑加白blackedhd,wwwhui4446com,yuppak@163.com,cwjswjswjs1,www.4158y.com,www.t3315.com,00381.com,www.hg033.com,138435345@qq.com,m.iptv221.com/itv.php,vns403.com,www.1775cc.com,www.82116.com,www.91pora.com,WWW.BET88.IM,seosey,WWW.HG8278.COM,www.m.61263322.com,wwwsbet8858com,帐号,www.277.cc,lilai365.net,www.77sihu.com,www.6626t. com,x3s2.com,ag6588cn,www.bbb466.com,m66388com,www.yf2826.com,www77733com,www.xpj8321.com,hg00549.cc,da55555.com,WWW.668K8.COM,4048icom,www705404com,88332203,QQah68. com,28365365.com,www97994com,18lkcom,9593lb.com,876800com,www.mt0888.com,vip1.8858.com,www121310net,9058376.com,wwwsb333net,9294com,www.www.vip2546.comwww.vip25755.com,www.72736.pw,www188226com,449013.com,www.w9609.com,www.aibise.com,防屏蔽地址發布頁 請加入收藏,www.61099.com,www.mgm9040.com,daheibiluntan,www.88-dr.com,www49z3com,www.156148.com,365.bm990.com,36299.com,www.6517728.com,www.ffkkk.com,c2580che,wwwbet9136com,36677ecom,00228hh.com,wwwbet57com,www.xpj89955.com,www.xpj2050.com,www.244uu.com,zt2013,5368182.com,kk866.com,lilingling00,60885.com,25ld.com,amvip779,shenyaotxtxiazai,800291com,mg1021.vip,81876s.com,899648com,www.vns1585.com,www.pj8456.com,ag85445.com,www.6998.com,www.j000222.com,www.yh135r.com,suyingcong,www.2282.hcom,www.111753.com,hh22me,www.88798aa.com,229333,www.837.am,www.baqizi.com,youfa5722com,www.189288.com,www.884ee.com,xq465.com,4809u.com,www5567com,wwwtt0009com,223aaa.com,www.pj2267.com,5583.ag,www.80878e.com,www.am222.com,402z1,g22776com,epaper.scnjnews.com,WWW.SUN3377.COM,c33377.com c77778.com b9158.c,www .zzz48.com,clinhuaping,www.bjgj222.com,q5z.wa8.xyz,www.bwin3099.com,4866a64.com,4455hhgz,123789.me,fs456,hg4030.com,834dabao.com|

以上会员名单排名不分前后