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# 用法向量求距离 - PowerPoint PPT Presentation

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P

C

D

O

B

A

1、已知正四面体P-ABC，棱长为1，求点P到平面ABC的距离。

AB=(2,-2,1), AC=(4,0,6)

∵ n·AB=0 2x-2y+z=0

n·AC=0 4x+6z=0

17

49

49

=

=

17

n

17

2、设A(2,3,1),B(4,1,2),C(6,3,7),D(-5,-4,8)

F(0,a,a),P(a/2,0,a/2)

z

-ax+ay=0

n⊥EF

M

F

ay-az=0

n⊥EB

∴n=(1,1,1)

E

P

3

a

n·PE

D

a

=

=

C

y

3

n

3

A

B

x

DA1=(1,0,1),AC=(-1,1,0)

z

x+z=0

n⊥DA1

D1

-x+y=0

C1

n⊥AC

∴n=(1,1,-1)

A1

B1

DA=(1,0,0)

3

1

n·DA

D

=

=

C

y

3

n

3

A

B

x

4、已知正方体ABCD-A1B1C1D1的棱长为 1，

(1)口答：直线A1D1与AB的距离；直线A1D1与AC的距离.

(2)求直线DA1与AC间的距离。

F(0,a,a),P(a/2,0,a/2)

z

-ax+ay=0

n⊥EF

M

F

ay-az=0

n⊥EB

∴n=(1,1,1)

E

P

P

3

a

n·PE

D

a

=

=

C

y

3

n

3

Q

A

B

x