选修2-1第三章-空间向量与立体几何-导学案

技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋～12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，1～7栋建筑层数为11层，8～12栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhills.236metersto2000metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5developmentofYibinlandscapesanddistinctivefeatureinthecenterofthecity,withlimitations,andspatialstructureoftypicalzonalgroup,2012-citiesinbuildingwithanareaofabout76.2km2.Fromcity-buildingsituation,oldtown-theSouthBankCenterconstructionislaggingbehind,disintegrationoftheoldcityisslow,optimizationandupgrading,qualitypublicserviceresourcesarestillheavilyconcentratedintheoldtowntogether.SouthbankCentrehasnotbeenformed,functionsoftheserviceareaspaceismissing.Meanwhile,peripheralgroupcentresservicewasweakandinadequateaccountingforcitydevelopment,suspiciouspatterncouldnotbeformed.Asregardstransport,withtheoutwardexpansionofcities,citieshavebeenexpanding,centripetalcitytrafficorganizationhasnotchanged,integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhills.236metersto2000metersabovesealevelinthecity,lowmountain,46.6%hills45.3%,pingbaonly8.1%.2.1.5developmentofYibinlandscapesanddistinctivefeatureinthecenterofthecity,withlimitations,andspatialstructureoftypicalzonalgroup,2012-citiesinbuildingwithanareaofabout76.2km2.Fromcity-buildingsituation,oldtown-theSouthBankCenterconstructionislaggingbehind,disintegrationoftheoldcityisslow,optimizationandupgrading,qualitypublicserviceresourcesarestillheavilyconcentratedintheoldtowntogether.SouthbankCentrehasnotbeenformed,functionsoftheserviceareaspaceismissing.Meanwhile,peripheralgroupcentresservicewasweakandinadequateaccountingforcitydevelopment,suspiciouspatterncouldnotbeformed.Asregardstransport,withtheoutwardexpansionofcities,citieshavebeenexpanding,centripetalcitytrafficorganizationhasnotchanged,§3.1.1空间向量及其运算学习目标1.理解空间向量的概念，掌握其表示方法；2.会用图形说明空间向量加法、减法、数乘向量及它们的运算律；3.能用空间向量的运算意义及运算律解决简单的立体几何中的问题．学习过程一、课前准备（预习教材P84~P86，找出疑惑之处）复习1：平面向量基本概念：具有和的量叫向量，叫向量的模（或长度）；叫零向量，记着；叫单位向量.叫相反向量，a的相反向量记着.叫相等向量.向量的表示方法有，，和共三种方法.复习2：平面向量有加减以及数乘向量运算：1.向量的加法和减法的运算法则有法则和法则.2.实数与向量的积：实数λ与向量a的积是一个量，记作，其长度和方向规定如下：(1)|λa|＝.(2)当λ＞0时，λa与A.；当λ＜0时，λa与A.；当λ＝0时，λa＝.3.向量加法和数乘向量，以下运算律成立吗？加法交换律：a＋b＝b＋a加法结合律：(a＋b)＋c＝a＋（b＋c）数乘分配律：λ(a＋b)＝λa＋λb二、新课导学※学习探究探究任务一：空间向量的相关概念问题：什么叫空间向量？空间向量中有零向量，单位向量，相等向量吗？空间向量如何表示？新知：空间向量的加法和减法运算：空间任意两个向量都可以平移到同一平面内，变为两个平面向量的加法和减法运算，例如右图中，OB，AB，试试：1.分别用平行四边形法则和三角形法则求,.ababa.b2.点C在线段AB上，且52ACCB,则ACAB,BCAB.反思：空间向量加法与数乘向量有如下运算律吗？⑴加法交换律：A.+B.=B.+a；⑵加法结合律：(A.+b)+C.=A.+(B.+c)；⑶数乘分配律：λ(A.+b)=λA.+λb．※典型例题例1已知平行六面体''''ABCDABCD（如图），化简下列向量表达式，并标出化简结果的向量：ABBC⑴；'ABADAA⑵；1'2ABADCC⑶1(')2ABADAA⑷．变式：在上图中，用',,ABADAA表示'',ACBD和'DB.小结：空间向量加法的运算要注意：首尾相接的若干向量之和，等于由起始向量的起点指向末尾向量的终点的向量，求空间若干向量之和时，可通过平移使它们转化为首尾相接的向量．2012年理科选修2-1◆高二第三章空间向量与立体几何月日班级：姓名：技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋～12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，1～7栋建筑层数为11层，8～12栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integratedenergy,chemicalsandtextileYibincity,arethethreecorepillarsoftheindustry.In2014,thewuliangyebrandvalueto73.58billionyuan,thecity'sliquorindustrysliptostabilise.Promotingdeepdevelopmentofintegratedenergy,advancedequipmentmanufacturingindustry,changningdistrict,shalegasproductioncapacityreached277millioncubicmetres,builtthecountry'sfirstindependenthigh-yieldwellsandpipelinesinthefirstsection,theleadinfactoryproductionandsupplytothepopulation.2.1-3GDPgrowthfigure2.1-4Yibin,Yibincity,Yibincity,fiscalrevenuegrowth2.1.4topographyterrainoverallisSouthwest,North-EasternState.Lowmountainsandhillsinthecitylandscapeasthemainridge-and-Valley,pingbasmallfragmentednaturepictureforwaterandthesecondlandofthesevenhil