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A 1. D 1. N. C 1. B 1. M. A. D. A. C. 数学作业. 1 、 如图所示,在长方体 ABCD-A 1 B 1 C 1 D 1 中 ,AB=5,AD=8,AA1=4, M 为 B 1 C 1 上一点且 B 1 M=2 ,点 N 在线段 A 1 D 上, A 1 D⊥AN. ( 1 )求 cos< >; ( 2 )求直线 AD 与平面 ANM 所成角的余弦值; ( 3 )求平面 ANM 与平面 ABCD 夹角的余弦值。. O 1. C 1. A 1. B 1. O. D.

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A1

D1

N

C1

B1

M

A

D

A

C

数学作业

1、如图所示,在长方体ABCD-A1B1C1D1中,AB=5,AD=8,AA1=4,

M为B1C1上一点且B1M=2,点N在线段A1D上,A1D⊥AN.

(1)求cos< >;

(2)求直线AD与平面ANM所成角的余弦值;

(3)求平面ANM与平面ABCD夹角的余弦值。


O1

C1

A1

B1

O

D

E

B

A

  • 2、在长方体OABC-O1A1B1C1中,OA=2,AB=3,AA1=2,E是BC的中点。

  • (1)求直线AO1与B1E所成角的余弦值;

  • (2)作O1D⊥AC于D,求点O与点D的距离。

C


M

F

E

P

C

Q

B

A

3、如图所示,已知四边形ABCD、EADM和MDCF都是边长为a的正方形,点P、Q分别是ED和AC的中点,求:

(1) 和 所成的角;

(2)P点到平面EFB的距离;

(3)异面直线PM与FQ的距离。


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