向量法解立体几何习题

熟悉建筑节能设计标准中有关暖通空调制冷部分、暖通空调制冷设备产品标准中设计选用部分、环境保护及卫生标准中有关本专业的规定条文。掌握上述标准中有关本专业的强制性条文。constructionworkareaintheformofconferencereviews.(2)reviewprogramreviewdateisdeterminedbytheprojectmanager;AccordingtotheprojectmanagerofprojectqualitycontrolDepartmentrequirespreparationofamanagementplan,representativeofthemanagementauditoftheproject,approvedbytheprojectmanager;ReviewProjectOfficeissuednoticesofmeetings;Projectmanagerfacilitatesthereviewmeeting,scheduledcontentunderreview;QualitycontrolDepartmentisresponsiblefortherecords,thepreparationofthereviewreportandcorrectiveactionplan,representativeofthemanagementauditoftheproject,approvedbytheprojectmanager;QualitycontrolDepartmentisresponsibleforthepreparationofrecordsandreportsthedistributionlist,orpublishtotheInternetbyengineeringpartoftheprojectstaffanddepartments.OrganizedbythequalitycontrolDepartmentisresponsiblefortrackingtheimplementationofcorrectivemeasuresinspections.3.4.5theoutputfromthemanagementreviewshallincludethefollowingelements:theeffectivenessandsuitabilityofthequalitymanagementsystem,whetheritbemaintainedandrevised;Qualitypolicyandqualityobjectivesareachievedandtomeetcustomerrequirements,whetheritbemaintainedandrevised;Theallocationofresourcestomeetrequirements,whetheryouneedtoaddoradjust.3.4.6correctiveactiontrackingandverificationontheissuesraisedinthereview,bytheprimaryresponsibilityofdepartmentsdrawupcorrespondingspecificcorrective,preventiveandcorrectivemeasures,andseriouslyimplemented.ProjectqualitycontrolDepartmentisresponsibleforthetracking,verificationandevaluationtheeffectofcorrectiveandpreventiveactions.3.4....(1)thesafetyprogramsanddepartmentsdealingwiththeformationofurbanspatialFEA'C'BB'CA向量法解立体几何1、四川19．（本小题共l2分）如图，在直三棱柱ABC－A1B1C1中，∠BAC=90°，AB=AC=AA1=1，延长A1C1至点P，使C1P＝A1C1，连接AP交棱CC1于D．（Ⅰ）求证：PB1∥平面BDA1；（Ⅱ）求二面角A－A1D－B的平面角的余弦值；2.(全国大纲文)如图，四棱锥SABCD中，AB∥CD,BCCD，侧面SAB为等边三角形，2,1ABBCCDSD．（I）证明：SD平面SAB；（II）求AB与平面SBC所成的角的大小。3、重庆文．（本小题满分12分，（Ⅰ）小问6分，（Ⅱ）小问6分）如题（20）图，在四面体ABCD中，平面ABC⊥平面ACD，,2,1ABBCACADBCCD（Ⅰ）求四面体ABCD的体积；（Ⅱ）求二面角C-AB-D的平面角的正切值。4、.（湖北文）如图，已知正三棱柱ABC-111ABC的底面边长为2，侧棱长为32，点E在侧棱1AA上，点F在侧棱1BB上，且22AE,2BF．（I）求证：1CFCE；（II）求二面角1ECFC的大小。5、、（2006年高考题）如图1，1l、2l是互相垂直的异面直线，MN是它们的公垂线，点A、B在1l上，C在2l上，MNMBAM。证明：NBAC。6、如图，直三棱柱A1B1C1—ABC中，D、E分别是BC、A1B1的中点.（1）证明：BE//平面A1DC1；（2）若AB=BC=AA1=1，∠ABC=90°求二面角B1—BC1—E的正切值.7、、如图，四棱锥ABCDP的侧面PAD垂直于底面ABCD,090BCDADC,22BCADPDPA,3CD,M在棱PC上，N是AD的中点，二面角CBNM为030。（1）求MCPM的值；（2）求直线PB与平面BMN所成角的大小。8、如图，在四棱锥SABCD中，底面ABCD为平行四边形，SA平面ABCD，2,1,ABAD7SB,120,BADE在棱SD上，且3SEED．（I）求证：SD平面;AEC（II）求直线AD与平面SCD所成角的大小9、如图所示，三棱柱'''CBAABC中，四边形''BBCC为菱形，oBCC60'，ABC为等边三角形，面ABC面''BBCC，FE、分别为棱'CCAB、的中点；（Ⅰ）求证：//EF面BCA'＇；（Ⅱ）求二面角BAAC'的大小。熟悉建筑节能设计标准中有关暖通空调制冷部分、暖通空调制冷设备产品标准中设计选用部分、环境保护及卫生标准中有关本专业的规定条文。掌握上述标准中有关本专业的强制性条文。constructionworkareaintheformofconferencereviews.(2)reviewprogramreviewdateisdeterminedbytheprojectmanager;AccordingtotheprojectmanagerofprojectqualitycontrolDepartmentrequirespreparationofamanagementplan,representativeofthemanagementauditoftheproject,approvedbytheprojectmanager;ReviewProjectOfficeissuednoticesofmeetings;Projectmanagerfacilitatesthereviewmeeting,scheduledcontentunderreview;QualitycontrolDepartmentisresponsiblefortherecords,thepreparationofthereviewreportandcorrectiveactionplan,representativeofthemanagementauditoftheproject,approvedbytheprojectmanager;QualitycontrolDepartmentisresponsibleforthepreparationofrecordsandreportsthedistributionlist,orpublishtotheInternetbyengineeringpartoftheprojectstaffanddepartments.OrganizedbythequalitycontrolDepartmentisresponsiblefortrackingtheimplementationofcorrectivemeasuresinspections.3.4.5theoutputfromthemanagementreviewshallincludethefollowingelements:theeffectivenessandsuitabilityofthequalitymanagementsystem,whetheritbemaintainedandrevised;Qualitypolicyandqualityobjectivesareachievedandtomeetcustomerrequirements,whetheritbemaintainedandrevised;Theallocationofresourcestomeetrequirements,whetheryouneedtoaddoradjust.3.4.6correctiveactiontrackingandverificationontheissuesraisedinthereview,bytheprimaryresponsibilityofdepartmentsdrawupcorrespondingspecificcorrective,preventiveandcorrectivemeasures,andseriouslyimplemented.ProjectqualitycontrolDepartmentisresponsibleforthetracking,verificationandevaluationtheeffectofcorrectiveandpreventiveactions.3.4....(1)thesafetyprogramsanddepartmentsdealingwiththeformationofurbanspatial1四川19如图，以A1为原点，A1B1，A1C1，A1A所在直线分别为x轴，y轴，z轴建立空间直角坐标系A1－B1C1A，则1(0,0,0)A，1(1,0,0)B，1(0,1,0)C，(1,0,1)B，(0,2,0)P．（Ⅰ）在△PAA1中有1112CDAA，即1(0,1,)2D．∴1(1,0,1)AB，1(0,1,)ADx，1(1,2,0)BP．设平面BA1D的一个法向量为1(,,)abcn，则11110,10.2ABacADbcnn令1c，则11(1,,1)2n．∵1111(1)2(1)002BPn，∴PB1∥平面BA1D，（Ⅱ）由（Ⅰ）知，平面BA1D的一个法向量11(1,,1)2n．又2(1,0,0)n为平面AA1D的一个法向量．∴12121212cos,3||||312nnnnnn．故二面角A－A1D－B的平面角的余弦值为23．2.(全国大纲文)20以C为坐标原点，射线CD为x轴正半轴，建立如图所示的空间直角坐标系C—xyz。设D（1，0，0），则A（2，2，0）、B（0，2，0）。又设(,,),0,0,0.Sxyzxyz则（I）(2,2,),(,2,)ASxyzBSxyz，(1,,)DSxyz，由||||ASBS得222222(2)(2)(2),xyzxyz故x=1。由22||11,DSyz得又由222||