当前位置:首页 >> 数学 >>878904com

WWW.303808.COM:高中数学人教a必修4评18 平面向量数量积的物理背景及其含义 含解析

fg99.com wwwbmw0778com c680616hgh 4239vip k6933com wb6340com js66857com

www.xpj1511.com cj0104 c29yy m.diai1.com www8059168com 999654.com mgm662com

学业分层测评(十八) (建议用时:45 分钟) [学业达标] 一、选择题 2 1.已知|b|=3,a 在 b 方向上的投影是 ,则 a· b 为( 3 A. 1 3 B. 4 3 ) C.3 【解析】 由数量积的几何意义知 D.2 2 a· b= ×3=2,故选 D. 3 【答案】 D 2.设 e1 和 e2 是互相垂直的单位向量,且 a=3e1+2e2,b=-3e1+4e2, 则 a· b 等于( A.-2 C.1 ) B.-1 D.2 【解析】 因为|e1|=|e2|=1, e1·e2=0, 所以 a· b=(3e1+2e2)· (-3e1+4e2) =-9|e1|2+8|e2|2+6e1·e2=-9×12+8×12+6×0=-1.故选 B. 【答案】 B 3.若向量 a 与 b 的夹角为 60°,|b|=4,且(a+2b)· (a-3b)=-72,则 a 的模为( A.2 C.6 ) B .4 D.12 【解析】 ∵(a+2b)· (a-3b)=a2-a· b-6b2 =|a|2-|a|· |b|cos 60°-6|b|2 =|a|2-2|a|-96=-72, ∴|a|2-2|a|-24=0, ∴|a|=6. 【答案】 C 4.(2016· 宁波期末)已知向量 a,b 满足|a|=2,|b|=1,a·b=1,则向量 a 与 a-b 的夹角为( 【00680056】 A. π 6 5π 6 |a-b|= (a-b)2= B. π 3 2π 3 3, ) C. D. 【解析】 a2+b2-2a· b= 设向量 a 与 a-b 的夹角为 θ,则 a· (a-b) 22-1 3 cos θ= = = ,又 θ∈[0,π], |a||a-b| 2 2× 3 π 所以 θ= .故选 A. 6 【答案】 A ) 5.已知点 A,B,C 满足||=3,||=4,||=5,则·+·+·的值是( A.-25 C.-24 【解析】 B.25 D.24 因为||2+||2=9+16=25=||2, 所以∠ABC=90°, 所以原式=·+(+)=0+·=-2=-25. 【答案】 二、填空题 6. 已知 a⊥b, |a|=2, |b|=1, 且 3a+2b 与 λa-b 垂直, 则 λ 等于________. 【解析】 ∵(3a+2b)⊥(λa-b), A ∴(λa-b)· (3a+2b)=0, ∴3λa2+(2λ-3)a· b-2b2=0. 又∵|a|=2,|b|=1,a⊥b, 1 ∴12λ-2=0,∴λ= . 6 【答案】 1 6 7. 已知|a|=|b|=|c|=1, 且满足 3a+mb+7c=0, 其中 a 与 b 的夹角为 60°, 则实数 m=________. 【解析】 ∵3a+mb+7c=0,∴3a+mb=-7c, ∴(3a+mb)2=(-7c)2,化简得 9+m2+6ma· b=49. 1 又 a· b=|a||b|cos 60°= ,∴m2+3m-40=0, 2 解得 m=5 或 m=-8. 【答案】 三、解答题 8.已知向量 a、b 的长度|a|=4,|b|=2. (1)若 a、b 的夹角为 120° ,求|3a-4b|; 5 或-8 (2)若|a+b|=2 【解】 3,求 a 与 b 的夹角 θ. ? 1? ? ? (1)a· b=|a||b|cos 120°=4×2×?- ?=-4. ? 2? 又|3a-4b|2=(3a-4b)2=9a2-24a· b+16b2 =9×42-24×(-4)+16×22=304, ∴|3a-4b|=4 19. (2)∵|a+b|2=(a+b)2=a2+2a· b+b2 =42+2a· b+22=(2 ∴a· b=-4,∴cos θ= 3)2, -4 1 = =- . |a||b| 4×2 2 a· b 2π 又 θ∈[0,π],∴θ= . 3 9.在△ABC 中,=a,=b,=c,且 a· b=b· c=c· a,试判断△ABC 的形状. 【解】 如图,a+b+c=0. 则 a+b=-c, 即(a+b)2=(-c)2, 故 a2+2a· b+b2=c2.① 同理,a2+2a· c+c2=b2, ② b2+2b· c+c2=a2. 由①-②,得 b2-c2=c2-b2,即 2b2=2c2, 故|b|=|c|. ③ 同理,由①-③,得|a|=|c|.故|a|=|b|=|c|, 故△ABC 为等边三角形. [能力提升] 1.(2016· 玉溪高一检测)已知|a|=2|b|≠0,且关于 x 的方程 x2+|a|x+a· b= 0 有实根,则 a 与 b 的夹角的取值范围是( ? π? ? ? A.?0, ? 6? ? ?π 2 ? ? ? C.? , π? ?3 3 ? 【解析】 ) ?π ? ? ? B.? ,π? ?3 ? ?π ? ? ? D.? ,π? ?6 ? 因为 Δ=a2-4|a|· |b|cos θ(θ 为向量 a 与 b 夹角). 若方程有实根,则有 Δ≥0 即 a2-4|a|· |b|cos θ≥0, 又|a|=2|b|,∴4|b|2-8|b|2cos θ≥0, 1 ∴cos θ≤ ,又 0≤θ≤π, 2 π ∴ ≤θ≤π. 3 【答案】 B 2.已知单位向量 e1,e2 的夹角为 60°,求向量 a=e1+e2,b=e2-2e1 的 夹角. 【解】 ∵e1,e2 为单位向量且夹角为 60°, 1 ∴e1·e2=1×1×cos 60°= . 2 1 3 ∵a· b=(e1+e2)· (e2-2e1)=-2-e1·e2+1=-2- +1=- , 2 2 |a|= a2= (e1+e2)2 = |b|= = 1 1+2× +1= 2 b2= 3, (e2-2e1)2 3, 1 3× 1 =- . 2 3 1 1+4-4× = 2 a· b 3 ∴cos θ= =- × |a||

以下是今天幸运会员获奖名单

www.907766.com,2835hcom,www.7282msc.com,wwwdbxylcom,www889,www.hg3903.com,333144com,www.mgm589.com,ks6651.com,www.68ps.com,8346lb.com,281885818@qq.com

koreansexscene28video asiat,www.treinsen.com,13331648877,www.jm0088.com,www940023com,169400,bo09com,www.rabysj.com,www ytav.com,7054.com,cc000111,15364659663s,2222ep.com,WWW.BS0034.COM,hg87.com,2021p.com,www.9560111.com,www.ds5666.com,00778ecom,www333,www.934435.com,ag3177vip,fun883,qy1225com,acdl152,22cca,com,youfa8986com,24777.com,pshangwu@163.com,www.8838499.com,WWW.R4.8878R.COM,se.97yes.com,www.460032.com,www.sc667.com,940hs. com,www.d26006.com,WWW.395234.COM,www.w6638.com,www.yeji337.vom,www.0006sb.com,www.ki368.com,www.621915.com,www.sunporno.com,ouzhouzuqiuzhishu,www.uuu779.com,www.l88.co,qs559,222128com,yb4578.com,www190902com,bbobiboyule,thz66. com,kdwin314,bo258,www.0659z.com,www.188ai.com,www.hhh053.com,www.vns65999.com,www.mm88f,w10010,beautiful198,www.qdxhedu.com,jsgw7.com,wwwac788com,a168a168,152749.com,tfa70,www.cdhsfs.com,www.556msc.com,wwwrb99com,qq1234qq,969yingyuan,www56733855com,www.362uc.com,www.7tav.com,58ys.org,2191671ms,WWW.599199.COM,ag0057.win,868327com,www.kf0808.com,yb5017com,www,5222,hg8319com,aaa196548,gzygzy1188,www.slr11.com,bmw8432,www.1779009.com,www.206666.com,www.cpk33.vip,kk78111,vns008.com,www5888999com,i3535. com,www.3478.com,www.7920x.com,js8700com,www623678com,www.7817623.com,jsc0077com,kkkk66,www.383.com,中小学生teeet,www.hjc0077.com,6313888.com,www.098176.com,y8915com,xpj8589.com,lei511225,www.732158.com,www.9535.com,7141eecom,www.349032.com,jnh556.com,咩測試07,WWWTTT661COM_WWW.TTT661,COM,as899420,863417com,lehu7728com,896310com,www.29ff.com,www755655com,wwweoplbcom,xmkankan@gmail,www.mblf8888.com,www.532970.com,hjc538.com,zunyi54.com,8520lb.com,www.ida889.tk,axx8878,www.3399760.com,www.t0222.com,526088749@qq.com,www.xpj4790.com,www.1446b.com,pj0365com,i2649.com,ljw694.com,wwwetwin588com,www6060zfcom,www.pocom,14888.cc,www8caicom,www.yb1872.com,cwww812708,8315lb.com,www.by6684..com,www.3999766.com,77655.com,wx137707,www.82267.com,nanrendaotiantangazai538xian,4767.win,rb742.com,www3333ezcom,vip33pj.cpm,www.jz413.com,wwwmsc570com,c1313455396,www655955com,www.dl99999.com,mng22m,www.75995.com,amvip111.com,WWW.16311.COM.CN,WWW.1DANJI.COM|

www.718048.com,967ii,wwwh9925com,848653com,www.723673.com,www.qile12.com,js00111.com,tt7676con,www.sb99e.com,www.wsdc114.com,877377com,www338696com,xvhong1234,wwwyf4000com,www.332255j.com,www.esb8.com,www.933325.com,www.pj159.com,www.gog888.coom,www.mgm5033.com,dxj1080. com,藏姬隔cjgdh最新入口,wwwmrb888com,zl5074com,1727382788@qq.com,https://m3u8.299du.com/m3u8/j,www.8899268.com,xiaojunliang,8408.cc,www.15sao.com,www.21365777.com,jjyy444,88134xyz,www.175hk.com,www777dcom,www.wns686.com,1931849818,xinzhizunyuledenglu,https://cmspapp40.xyz/,mh0008.com,wwwxpj5753com,ag2252com,www39408com,pj88l,beastysexlinks.com,www.m.kkppdd,wxc497,www.shiliu66.com,wwwbet6407com,ts064,WWW.563MSC.COM,vipa126xyz,www4795com,was6666.com,www.88844.com,1422.com,WWW.4377.COM,www.pu690.com,WWW.4179.COM,www.hsbet88.com,www778876com,48084808.cc,www.vn88007.com,9119999.com,www.180551.com,www.8839f.com,www.151528.com,www.5549.net,880894.com,WWW.773773.COM,m.xeacg.net,www.aj@77.168.com,www.547567.com,www.225yu.com,www.bodog99.com,www0281com,4866c66,qy7906com,WWW.452233.COM,www640067com,81544.com,www.aa9830.com,www935aa,qdcp10086.com,WWW.HG2749.COM,www.k558668.com,www.951815.com,m.wb00678.com,www.77225.com,ag84063.com,z77gg,www.778778.cow,www.243h2.com,56568.com,adcwangzhizaixianguankan,www. 696hs,c7645754957,www.8870178.com,www.dzcf.com,blr9955.com,83456com,duzhantianyatxtxiazai,kansqi,long5,sz992,384455..com,jinshiguojiwangzhi,www.0907.ent,xin988,WWW.BT3344.COM,bet0119.com,ceucuduf,www.25711.com,wwwle678cc,naxiewangyouyoudubo,WWW.EBEB123.COM,thm121,qin5751,xxxx8888,www.xpj55054.com,www.hg1269.com,www.b88997.com,最新双色球一码定蓝,www.089452.com,hg8438com,www.chinabett.com,wwwule607com,qgspjx.com,www.hg689977.com,chenyuan,lincangjian,cwys1462060,www.x5310.com,www.mg9503.com,wwwwd0002com,www.nm12333.cn,www8884ylcom,meinvluoxiongwuzhedang,9388a.com,lsnb14.com,www.yhw86.com,wwwpj638com,HGVIP3COM,WWW702555COM,wwwyinlian000,wbl999.com,g788.com,tt5688com,952700,www.igcp.com,WWW.BBB337.COM,www.6xh6.com,www.gp,kdh970pw,ag4647com,www.jsdc995.com,xinchang120,8888807.net,www. 2019.com,mcm.edu,99ff9. com,s163163.com,www.77809.com,www.233.166.co,www.lx5555.com,www028987com,m.agm8383.com,mmmm4466|

xh3330.com,mj999,www0967009com,wwwjsdc51com,wwwczhotnet,2463913473@qq.com,www.435222.com,www.sku520.com,wwwi33318com,805111,www80711com,www.3808z.com,hj351,wushoufeikanwuwangzhanwanzheng,avjinri.com,www.gj1688.net,hg7717com,22555.com,847989com,www.1789666.com,WWW.X55888.COM,www155unet,www.449018.com,www.46333.co,www.ewf6.info,2061405.com,www.hgbet666.com,www.034ee.com,yabovip8376com,jinminxu521,13978542919,lon1239,xiaojing,kk55kknet,www.p333jj.com,www340340vip,12axax永久地址,derong82@sina.com,71199vnscom,ag5818、com,wt138.com,eee678com,aa8480,www.yinmb.com,13199m.com,www.237432.com,1936897932@qq.com,bmw198.com,www.578833.com,www.1234qu.com,wwwvns59333com,15Pqianbailumenglixuntaqianbailu,www.wlilai123.com,776588zcom,16685133655,www.lh6.org,www.311msc.com,52256.com,www4868com,www.yezhulu.me,zr4333.com,6662012.com,www.528bb.com,ljw958.com,www.665888005.com,www99844com,www.6686894.com,2544r76com,WWW.HG4007.COM,2453z,www.1122cr.com,fai69com视频直播,9a000.com,808628.com,26k66.com,www.566670022.com,608555.com,xianfenghenhenaiyeyeluwangzhi,kedouzaixianguankan,www.254353.com,sss0094com,ash732,wwwesb999org,wwwhg0517com,www.666717.com,www.sb0081.com,www.hg651.com,www.2233kk332233.com,6245cc,www.359.com,www.0151gg.com,d28338.com,ag8060com,www.js90333vip.cc,liujiabei,wj963,yb0934.com,352200.cc,gmail.com,5c5c5c5c.com,817735com,tangmengxia,agks0741com,ag4244vip,www.xpj1168.com,jiao00000,www.www.5043.com,qy1899.com,jinnuxi,lovelifefurniturehandles.com,zt. hk,WWW74011COM,ag6009.com,h6686.net,www.4786a.com,www.hntjpx.com,www.gwsmwj.com,2481004423@qq.com,wdylc.com,15085130779,wwwbg947com,huang999,397377.com,189930,www.98005.com,www.340567.com,letianyulepingtaizhuce,sswuon,7244hu.C0M,www.mgm11566.com,wwwy4848cc,hg08net,www.9121218.com,dan522,www路77766路com,www.333vip.com,nc088com,www771456com,httpwww2clsscom,yangde321,www.510817.com,www.www-pj525.com,www.5475g.net,999aaa,894692com,www.g7408.com,WWWag64999ecom,www.gao84841.com,www.hk158.net,www.222zr.gs,10365com,1259,wwwhg2826com,se52ss.net,金堆城吧,www005235com,www3384cc,hjjb11.wang,8846,com,www.sb8122.com,www.456gan.com,www.51ttfl.com,WWW.778050.COM,www.7843ss.com,WWW.01YLG.COM,azmat123520.89919.com,ckcool,bmw8389|

www.vns0975.com,xpj8062com,www7766bcom,www.b98888.com,yjd8.com,442288com,www77440168com,www.1155p.com,ku879,920meimei最新网址,zhao108hh,www.37cc.com,wwwhg99678com,yb1759.com,oumeikaifangluotitupian,www.515hh.com,qq275365936,www.yt8000.com,www.579505.com,dzj0091com,www938hk,jingziwo发布页,www.18197.com,zhangguohui,www42579gcom,www.33121a.com,WWW.2016BR.COM,www.27889x.com,t444c,895509com,www.wns2049.com,WWW.320.COM,amyh.com,www,650hu,com,745msccom,Www559tacom,www.47juju.com,www.44av.com,www.hj8789.com,www.jdzxcc.com,z6.com,www.pp5002.com,caoporndizhi,www.yh8374.com,905829033,www.1012234.com,www.893824.com,www.2599p.cc,aqd2222.com,WWW.HG0432.COM,www.44c58.com,www.309456.com,www8081768com,ve125q,k04222.com,qy6753com,www.993qq.com,849877com,hg2260com,www.ff8876.com,WWW.30895.COM,WWW.XDL004.COM,www.j541.com,017xie.com,qq123qq,dd518,q797827,sesese9911在线视频,www.7890200.com,js8470com,003004sc.com,wwwkzwcjrcom,www.987hh.com,hg7836com,33000.com,yb4530com,wwwbet249com,www.9987.com,883DCOM,买车一年后发现养不起,wwwwww-039vip,815345.com,zyg8888,744646360@qq.com,dianzier,yabo3153.vip,www.83suncity.com,www.519871.com,hanhui,wwwxpj599com,WWW.911TY.COM,www030552com,3654010.com,www.155655.com,www035006com,nss88888,www.oso100,btbdydh,qyy3305com,wwwmuredscom,www.870289.com,mcc202,xpj9066.com,licepk,www.mensuozx.com,www.474556.com,www. v 4d 5.com,www.3842.com,liushiyou,www.231055.com,jjgirls,www4084com,wwwjxcbccom,www.gzmazda.com,wwwhy376com,www.ys885.com,155324381@qq.com,k1z.wa8.xyz,wwwhg9675com,www.337357.com,www.c8810.com,www.xpj99966.com,yy181898,www.850739.com,ffhg5588,mg5837.com,hg00291.com,OSU MUSIC OZF2,c19831223m,www.sun777.com,jl22222.com,www.xpj516.com,67877x.com,www.toutouyao.com,www.dizhi1.com,www.596sunbet.com,8eeg.com,日本老汉推车网站,97575f.com,www583645com,www.6885m.com,800184com,www.st118.com,lh4942.com,vw035.com,今晚特开,wwwj787com,www.059.com,fa32443,pp1100.com,www.317828.com,cherry,9946t.com,zhengchao,www.sb9899.com,6670.com,g165.net,jsgw555com,www.da88988.com,www.m.6hewawa.com,6123010,10050826,abc06200923,sun631fww,m.lilai5.vip,wwwyh41888com,wwwjs2433com,hg128z|

以上会员名单排名不分前后