II

f (x,y,z) =0

1. x,y,z

2.

f(x,y,z) -

R (x0,y0,z0)

(x-x0)

2+(y-y0)2+ (z-z0)

2=R2.

R x2+y2+z2=R2.

x2 +2x+y2-4y+z2=4.

:

f1(x,y,z)=0, , f1(x,y,z)=0 1 f2(x,y,z)=0. f2 (x,y,z)=0 2

1 2

xyz R

(x-a)2+(y-b)2+(z-c)2 R2

na , -

)

Ax+By+ Cz +D=0

A2+ B2+ C2 0

Oxyz

n (A,B,C)

Ax+By+Cz+D=0 . A(x-x0)+ B(y-y0)+ C(z-z0)=0

:

Ax+By+Cz+D=0 n

B,C,D

Ax+By+Cz+D=0

By+Cz+D=0 Ox

Ax+Cz+D=0 Oy

Ax+By+D=0 Oy

By+Cz=0 Ox

Ax+Cz+D=0 Oy

C=0, D=0

Ax+By+D=0 Oz

A=0, B=0

Cz+D=0

Oxy

By+D=0

Oxz

Ax+D=0

Oyz

A=0, B=0

Cz=0 Oxy

C=0, D=0

By=0 Oxz

C=0, D=0

Ax=0 Oyz

a, b, c (

1z

z

b

y

a

x.

A (7;- Oxz

:

1 : A1x+B1y+C1z+D=0

2 : A2x+B2y+C2z+D=0

22

22

22

21

21

21

212121cosCBACBA

CCBBAA

:

1n (A1;B1;C1) 2n (A2;B2;C2)

A1A2+B1B2+C1C2=0

1 :A1x+B1y+C1z+D=0

2 :A2x+B2y+C2z+D=0

2

1

2

1

2

1

2

1

D

D

C

C

B

B

A

A

2

1

2

1

2

1

2

1

D

D

C

C

B

B

A

A

1 2

A,B,C

x-y+2z+15 =0 5x+9y-3z-1=0

.