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用向量法求 二面角

用向量法求 二面角. 例 1 : 在三棱柱 ABO —A 1 B 1 O 1 中 , 平面 OBB 1 O 1 ⊥ 平面 OAB,∠ O 1 OB=60 0 , ∠B OA=90 0 ,OB=OO 1 =2, AO= . 求. z. O 1. B 1. (1) 二面角 O —AB—O 1 的大小. A 1. O. B. A. y. x. 例 2 : 已知四棱锥 P —ABCD,PB ⊥AD, 侧面 PAD 为边长等于 2 的正三角形 , 底面 ABCD 为菱形 , 侧面 PAD 与底面 ABCD 所成的二面角为 120 0 .

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用向量法求 二面角

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  1. 用向量法求 二面角

  2. 例1:在三棱柱ABO—A1B1O1中,平面OBB1O1⊥平面OAB,∠O1OB=600,例1:在三棱柱ABO—A1B1O1中,平面OBB1O1⊥平面OAB,∠O1OB=600, ∠BOA=900,OB=OO1=2,AO= . 求 z O1 B1 (1)二面角O—AB—O1的大小 A1 O B A y x

  3. 例2:已知四棱锥P—ABCD,PB⊥AD,侧面PAD为边长等于2的正三角形,底面ABCD为菱形,侧面PAD与底面ABCD所成的二面角为1200.例2:已知四棱锥P—ABCD,PB⊥AD,侧面PAD为边长等于2的正三角形,底面ABCD为菱形,侧面PAD与底面ABCD所成的二面角为1200. (1)求P到底面的距离 z P F G 1.5 C D (2) 面PAB与面CPB所成二面角的大小 O H x B A y

  4. 例3:如图:以点O(0,0,0),A(4,0,0),B(3,2,0) P(1,4,1)为顶点的空间几何体中，R,S是PA 的三等分点,M,N分别是PB,OB的中点,求 (1)直线NR和MS的夹角 (2)二面角P-OA-B的大小 《名师》Ｐ79 考点３ D C

  5. 练习1：若正四棱锥P—ABCD的侧面是正三角形。求练习1：若正四棱锥P—ABCD的侧面是正三角形。求 (1)侧面PAB与底面ABCD所成的二面角 (2)侧面PAB与侧面PBC所成的二面角 (3)侧面PAB与侧面PCD所成的二面角

  6. 练习2:在底面为直角梯形的四棱锥S—ABCD中, ∠ABC=900,SA⊥平面ABCD, SA=AB=BC=2,AD=1.求平面SCD与平面SAB所成二面角. z S y C B A D x

  7. 作业： 1.(2001年高考题)如图,以正四棱锥V—ABCD的底面中心O为坐标原点建立空间直角坐标系O—xyz,其中ox//BC,oy//ab.E 为ＶC的中点.底面边长为2a,高为h z V E (2)若∠BED是二面角B—VC—D的平面角,求∠BED C D O y A B x

  8. 2.(2004年浙江高考题)如图,已知正方形ABCD和矩形ACEF所在的平面互相垂直, AB= ,AF=1,M为EF的中点. (1)求证:AM//平面BDE. E (2)求二面角A—DF—B的大小 M F B C D A

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