2016年空间向量与立体几何单元练习题.pdf

1 空间向量与立体几何习题一、选择题每题5 分，共 50 分1.如图，在平行六面体 ABCDA1B1C1D1中，M 为 AC与 BD 的交点.假设11BA=a，11DA=b，AA1=c，则以下向量中与MB1相等的向量是A.21a+21b+c B.21a+21b+cC.21a21b+c D.21a21b+c2.以下等式中，使点 M与点 A、B、C一定共面的是A.OCOBOAOM23 B.OCOBOAOM513121C.0OCOBOAOM D.0MCMBMA3.已知空间四边形 ABCD 的每条边和对角线的长都等于1，点 E、F 分别是 AB、AD 的中点，则DCEF等于A.41 B.41 C.43 D.434.假设)2,1(a，)1,1,2(b，a与 b 的夹角为060，则的值为1 C 5.设)2,1,1(OA，)8,2,3(OB，)0,1,0(OC，则线段 AB 的中点 P 到点 C 的距离为A.213 B.253 C.453 D.4536.以下几何体各自的三视图中，有且仅有两个视图相同的是ABCD7.右图是一个几何体的三视图，根据图中数据，可得该几何体的外表积是正方体圆锥三棱台正四棱锥2 A.9B.10C.11D.128.如图，ABCD-A1B1C1D1为正方体，下面结论错误的选项是A.BD平面 CB1D1 B.AC1BDC.AC1平面 CB1D1 D.异面直线 AD 与 CB1所成的角为 609.如图，在长方体ABCD-A1B1C1D1中，AB=BC=2,AA1=1,则 BC1与平面 BB1D1D所成角的正弦值为A.63B.552C.155D.10510.ABC 的三个顶点分别是)2,1,1(A，)2,6,5(B，)1,3,1(C，则 AC边上的高 BD长为A.5 B.41 C.4 D.52二、填空题每题5 分，共 20 分11.设)3,4,(xa，),2,3(yb，且ba/，则 xy .12.已知向量)1,1,0(a，)0,1,4(b，29ba且0，则=_.13.在直角坐标系xOy中，设 A-2，3，B3，-2 ，沿x轴把直角坐标平面折成大小为的二面角后，这时112AB，则的大小为14.如图，PABCD 是正四棱锥，1111ABCDA B C D是正方体，其中2,6ABPA，则1B到平面 P AD 的距离为 .三、解答题共80分俯视图正(主)视图侧(左)视图2 3 2 2 文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M13 15.本小题总分值12 分如图，在四棱锥P-ABCD 中，底面 ABCD 是边长为 1的正方形，侧棱 PA的长为 2，且 PA与 AB、AD的夹角都等于 600，M 是 PC的中点，设cbaAPADAB,1试用cba,表示出向量BM；2求 BM 的长16.本小题总分值14分如下的三个图中，上面的是一个长方体截去一个角所得多面体的直观图，它的正视图和侧视图在下面画出单位：cm.1在正视图下面，按照画三视图的要求画出该多面体的俯视图；2按照给出的尺寸，求该多面体的体积；3在所给直观图中连结BC，证明：BC 面 EFG.17.本小题总分值12分如图，在四面体ABCD 中，CBCDADBD，点EF，分别是 ABBD，的中点求证：1直线/EF面 ACD；2平面 EFC面 BCD 224侧视图正视图624GEFCBDCABDMPDCBA文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M14 俯视图侧视图正视图121121EDCBAP18.本小题总分值 14 分如图，已知点 P在正方体DCBAABCD的对角线BD 上，PDA=60.1求 DP 与CC 所成角的大小；2求 DP 与平面DDAA所成角的大小.19.本小题总分值14分已知一四棱锥 PABCD 的三视图如下，E 是侧棱 PC上的动点1求四棱锥 PABCD 的体积；2是否不管点 E 在何位置，都有 BDAE？证明你的结论;3假设点 E 为 PC 的中点，求二面角 DAEB 的大小20.本小题总分值 14 分如图，已知四棱锥PABCD，底面 ABCD为菱形，PA平面 ABCD，60ABC，EF，分别是 BCPC，的中点1证明：AEPD；2假设 H 为 PD上的动点，EH 与平面 PAD 所成最大角的正切值为62，求二面角 EAFC 的余弦值P B E C D F A DCBAPDCBA文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M15 练习题参考答案一、选择题1.)(21111BCBAAABMBBMB=c+21(a+b)=21a+21b+c，故选 A.2.1),(zyxRzyxOCzOByOAxOMCBAM且四点共面、由于MCMBMAMCMBMACBA0由于都不正确、选项.)()()(共面使所以存在MCMBMAMCyMBxMAyx,1,1四点共面，、为公共点由于CBAMM故选 D.3.的中点分别是ADABFE,BDEFBDEFBDEF21,21/且,41120cos1121,cos21210DCBDDCBDDCBDDCEF故选 B.4.B 5.B 6.D 7.D 8.D 9.D 10.由于4,cosACACABACABABAD，所以522ADABBD,故选 A 二、填空题11.9 x 轴于 C，BD x 轴于 D，则DBCDACABcos6)180cos(,0,0,2,5,30DBACDBACDBCDCDACDBCDAC000222222222120,1800.21cos),cos600(2253)112()(2)(由于ACDBDBCDCDACDBCDACDBCDACAB14.以11BA为x轴，11DA为y轴，AA1为z轴建立空间直角坐标系设平面 PAD 的法向量是(,)mx y z，(0,2,0),(1,1,2)ADAP，02,0zyxy，取1z得(2,0,1)m，1(2,0,2)B A，1B到平面 PAD 的距离1655B A mdm.文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M16 三、解答题15.解：1 M 是 PC的中点，)(21)(21ABAPADBPBCBMcbaacb212121)(2122,1,2,1cbaPAADAB由于160cos12,0,60,00cbcabaPADPABADAB由于),(21cbaBM由于23)110(221141)(241)(4122222222cbcabacbacbaBM2626的长为，BMBM.16.解：1如图2 所求多面体体积VVV长方体正三棱锥11446222322284(cm)33证明：在长方体 ABCDA B C D 中，连结 AD，则 ADBC因为 EG，分别为 AA，AD 中点，所以 ADEG，从而 EGBC又 BC平面 EFG，所以 BC 面 EFG 17.证明：1E,F 分别是 ABBD，的中点，EF 是ABD 的中位线，EFAD，AD 面 ACD，EF面 ACD，直线 EF面 ACD；2ADBD，EFAD，EFBD，CB=CD，F 是的中点，CFBD 又 EF CF=F,BD面 EFC，BD面 BCD，面 EFC面 BCD.A B C D E F G ABCD文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M17 18.解：如图，以 D 为原点，DA为单位长建立空间直角坐标系Dxyz则(10 0)DA，(0 01)CC，连结 BD，B D 在平面 BBD D 中，延长 DP 交 B D 于 H 设(1)(0)DHmmm，由已知60DH DA，由cosDA DHDA DHDA DH，可得2221mm解得22m，所以22122DH，1因为22001 1222cos212DH CC，所以45DH CC，即 DP 与 CC 所成的角为452平面 AAD D 的一个法向量是(0 1 0)DC，因为22011 0122cos212DH DC，所以60DH DC，可得 DP 与平面 AAD D 所成的角为3019.解：1由该四棱锥的三视图可知，该四棱锥PABCD 的底面是边长为1的正方形，侧棱 PC底面 ABCD，且 PC=2.1233PABCDABCDVSPC(2)不管点 E 在何位置，都有BDAE 证明如下：连结 AC，ABCD 是正方形，BDAC PC底面 ABCD 且 BD平面 ABCD BDPC 又 ACPCCBD平面 PAC 不管点 E 在何位置，都有 AE平面 PAC 不管点 E 在何位置，都有 BDAE(3)解法 1：在平面 DAE 内过点 D 作 DGAE 于 G，连结 BG CD=CB,EC=EC，Rt ECD Rt ECB，ED=EB AD=AB，EDAEBA，BGEA DGB 为二面角 DEAB 的平面角BCDE，ADBC，ADDE 在 RADE 中AD DEDGAE=23=BG 在DGB 中，由余弦定理得212cos222BGDGBDBGDGDGBA B C D P ABCDx y z H 文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6M1文档编码:CH6K7H10K4U1 HI5A1K1B6G5 ZP4U8Z2Q6