Добавил:

Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Национальный минерально-сырьевой университет «Горный»

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

attachments_22-12-2011_21-07-09 / semestr1_1

.pdf

Скачиваний:

Добавлен:

02.04.2015

Размер:

1.03 Mб

Скачать

☆

<<< < Предыдущая 1 2 3 4 5 6 7 8 910 / 1210 11 12 > Следующая >>>

,. 3.16

2. $# ! # 5 4

2 (3.17)

D66 = 2I, , 2

2 7 ( D ), 2 A 23

A		x		y		z
y			+		+		= 1,		(3.18)
		a		b		c

a = D/A,	b = D/B,						c = D/C .		& #
(3.18)								I
! "#		5 4".						4	3,

A 2 2 a,b,c		2 A , 2 3
7 ( . 3.16).
3.	$#	!, 4 L			5	5 &: &
! & # &
% 3 M0 (x0 , y0 , z0 ) , 2 4 H 7 2 P ,
A 2 D 2 n = (A, B,C) ( . 3.17).
!27	4		M (x, y, z)	2		P		n
M0M = (x x0, y y0, z z0 ) ,			2 4 H		2		P ,	A

27. 2 A 27 M0M n 7 27 7

2I 27 7

z		n				M0M n = 0.
z				2		7A 23 7		A
				2		7A 23 7		A
		M0		, , D
		M0					6 A,	2 A
	P

			M	2 P :
				2 P :
				A(x x0 ) + B(y y0 ) + C(z z0 ) = 0.					(3.19)


	r0	r		2		A -
		r			r0 r M0			M ,
					r0 r M0			M ,
x			y	2	27			A 4
	.	, 3.17	y	3
	.	, 3.17		3
					(r r0 ) n = 0 .				(3.20)
% 2 - D & #						! # #
.			4. $#		!,		4 L 5
			4. $#		!,		4 L 5
		b	5 &: & !! ! #&
		b	!! % #
			!! % #						P ,
	M0	M		A			2		P ,
	a		7H				I
	a		M0	(x0 , y0 , z0 )		22 23			A
P			M0	(x0 , y0 , z0 )		22 23			A
P	, 3.18
.	, 3.18			90
				90

22 A A		a(a1, a2,a3)			b(b1,b2,b3) ( .3.18). 2 A
2 4	23				M	2	P 7 27 7
			r	A A 2
A 2 3 M0M ,a,b ,				A A 2
7 27 7 2I A 5 7, 3
		( M0M		r
		( M0M		, a,b) = 0.
0 7A 23 D A
			x x0	y y0	z z0
			x x0	y y0	z z0
			a1	a2	a3	= 0.	(3.21)
			b1	b2	b3
5. $#	!, 4 L 5 , ! * L
		C1 (x1 , y1 , z1 ) ,			C 2 (x2 , y2 , z2 )		M0 (x0 , y0 , z0 ) ,
% 3		C1 (x1 , y1 , z1 ) ,			C 2 (x2 , y2 , z2 )		M0 (x0 , y0 , z0 ) ,

2 4 H 2 ( . 3.19). A

2. @ 2 7

H A, 2 a

M0 M

. , 3.19

b 7 3, A, M0C1 0 2 A

x x0	y y0	z z0
x x0	y y0	z z0
x1 x0	y1 y0	z1 z0	= 0.
x2 x0	y2 y0	z2 z0

M0C2 .

(3.22)

6 5! % # % & #				#	#
1. ,'L & #	#
#						H1	l
2 7A 7 7 27 7 A
2 P1 P2 ,	7					H2
A1x + B1 y + C1z + D1 = 0 A2 x + B2 y + C2 z + D2 = 0 ,
( .3.20), D 7A I A 4						,. 3.20
3 A , A						,. 3.20
'L & # 7A:
l	A1x + B1y + C1z + D1 = 0,
l	A x + B y + C z + D					= 0.	(3.23)
s		2	2	2	2
s
M	2. 8-			& #
	2. 8-			& #
M0	#	#
M0	% 3 l - 23 7 7A 7. 2 4
	% 3 l - 23 7 7A 7. 2 4
			27 7
.3.21,	91

M0 (x0 , y0 , z0 ) , 2 4 H 7A, A s = (m, n, p) , 22 23 A D 7A ( .3.21). 0 s 7 #! :L # . 2 M (x, y, z) - 23 7 7A l , M0M s

22. % 22 H H 2 t ,

r
M0M = ts.
2 A - r0 r M0	M , D
6 A 2 A 4 3
r r0 = ts.	(3.24)

(3.24) I 7 #- A

7A.

3. " & # #

% 5 A 2 5 (3.24) 6 A, A

5 A 23 x, y, z 2 A & # 7A:

x = x0 + mt,
	+ nt,	(3.25)
y = y0
	+ pt.
z = z0

7 ' ' 5 7A

2 7A 2 A 7A.

2 3 22

6 A, 2 A & # 7A:

x x0	=	y y0	=	z z0	.
m		n
				p

2 -2 ' A 2 (3.26) 2I, 2I ' 2 IH 2 23.

4. $# 5 # #

!27 7 7A, 7H

M0(x0, y0, z0) M1(x1, y1, z1) ( . 3.22),

23 A 22 :

M0M = (x x0, y y0,z z0) M0M = (x1 x0, y1 y0,z1 z0) ,

M (x, y, z) - 23 7 7A:

(3.26)

' A, '

l C0

,. 3.22

x x0	=	y y0	=	z z0	.	(3.27)
		y1 y0
x1 x0				z1 z0
		92

		$7!%
1. $7 ! * & % #			#
$7! * & % l1 l2			I A 35 2, '
7A A l1 l2 .
		l1		l1
	r		r	r
	s1		s2	s1
	!			!
	r
	s2	l2		l2
		l2		l2
)		.	, 3.23	')
		.	, 3.23

, 2 A 4 7A A 27IH A A 2 '

, 2 ' 2 I 7 2 ' ( .3.23). , 23 7

27 7 , 27 2 A 4 7A A 2 A

cos! =

2. $7 ! * &

! : # #

$7! * &

! : 7 2 A 4 7A = I

2 3 ( .3.24).

	r	r
	s	s
	r1	r2	.	(3.28)
	r1	r2	.	(3.28)
\| s1 \|\| s2 \|

n s

sin = sin(90o ) = cos ,

,. 3.24

- 2 A 4 A 23 A

A 2 n 27IH A A s 7A. 2 23,

				r	r
		sin =		n s			.			(3.29)
		sin =		r	r		.			(3.29)
			\| n \|\| s \|
H1	n2	3. $7 ! * &						!
"		$7! " * & #&							! H1 H2
"		A			A 35					2,
H2	n1	' D A							2 7A.	2
		2				22 23,			2	2

	,. 3.25	7 2I.
	,. 3.25	94
		94

, A 2 A 23

2, cos" =| cos

| ,

A 4

A 23 A A

2 ( . 3.25).

cos " =

(3.30)

| n1 || n2 |

4. 6 * & #& #

, 7

A 4 A7 A

M0 (x0 , y0 , z0 )

M1(x1, y1, z1)

A 4 2 3 2 M1M0 . #

M1M 0 = (x0 x1, y0 y1, z0 z1) , 2

uuuuuuur

l =

(x0 x1)2 + ( y0 y1)2 + (z0 z1)2

M1M 0

(3.31)

5. 6 #

# !

% 3

M0 (x0 , y0 , z0 )

2 3

P ,

Ax + By + Cz + D = 0 . % 7 A S

2 A 7 2 27 C0C,

H 2 3 ( . 3.26),

7 27 7 6 A 2

,. 3.26

S =

| Ax0 + By0 + Cz0

+ D |

(3.32)

A2 + B2 + C2

6. 6

% 7 A

M0(x0, y0, z0)

A 7 2

27, H 7A I, 27IH

s . 0 3A A 23 I 7A M1(x1, y1, z1) ,

	r	M1M0
	r
d =	s ×				.	(3.33)
		r	\|
		r
		\| s
6 K				#
" 1. 2, 7H						A( 1,2,1)
27 n(2,2, 4) .
6 K. (3.19) 27 5 2 7 A
2(x +1) + 2(y 2) 4(z 1) = 0.
, 7 ', 2 A
2x + 2y 4z + 2 = 0		2 x + y 2z +1 = 0 .

: A 2 A x + y 2z +1 = 0 .

" 2. 2, 7H A(1, 1,3)

, B(2,0, 1) , C(5,2,1).

6 K. % A (3.22):

x 1	y +1	z 3
x 1	y +1	z 3
2 1	0 ( 1)	1 3	= 0.
5 1	2 ( 1)	1 3

% 2 7 2 27 7 ' 2 2 A

2: 10x 14y z 21= 0.

: A 2 A 10x 14y z 21= 0. " 3. 3 7 7A, 7H

A(2,1,3) B(4,5,3).

6 K. 0 M0

' A 23 3 A,

27IH 7A - AB = (2, 4,0) . # 7

7A D A 2 A I :

x 2

y 1

z 3

% A 3 D 5 2 A

x 2

y 1

z = 3.

x 2

y 1

: A 7 7A A I

, z

= 3.

" 4.

2x y + 3z + 3 = 0

7A,

M0 (1,2,1)

22 23

s = (2,4, 2) .

6 K. % A 7 7A A I :

x	=	1+ 2t
	=	2 + 4t.
y
	=	1 2t
z

# 7 M (x, y, z) 7A 2 2 7I

A I 2 7A 7A. % A x, y z 7A 2, 2 A:

2(1+ 2t) (2+ 4t) + 3(1 2t) + 3 = 6t + 6 = 0.

I t = 1 A 4 7, 277 D

7 7A: M(3,6, 1) .

: 7 2 7A M(3,6, 1) . " 5. % 7A 7 'H A 7A:

	x y + z 2	=	0
		5 =	.
2x + y 2z +		5 =	0
	96

7 D 7A.

6 K. " 2I 7 2 23 A A x y, 2 A:

3y 4z + 9 = 0 3x z + 3 = 0 .

0 A A I z ' 7 A 2

23:

		x +1		=		y + 3		=		z	.
		1		=				=			.
		1		4				3					x +1		y + 3		z
													x +1		y + 3		z
: 7 7A A I														=		=		.
: 7 7A A I													1	=	4	=	3	.
" 6. 2 2 A 4 7A l1 ,
A 7A:
	x 1		=		y 2		=		z 1			,
	5		=		4		=		3			,
	5				4				3

7A l2 , 'H A 7A:

2x y + z + 3 = 0,

x y + z + 5 = 0.

6 K. A 27IH s2 7A l2

A 23 2:

		r	r	k
		r	r
r		i	j		r	r	r
r					r	r	r
s2	=	2	1	1	= 0i	j	k.
		1	1	1

% A 27IH 6 A 2 (3.28):

cos! =

5 0 + 4

( 1) + 3 ( 1)

52 + 42 + 32

+ ( 1)2 + ( 1)2

: 2 2 A 4 A 7A A arccos (

) .

" 7. 7 M0(3, 2,1) 7A l1 ,

A 7A

y + 5

x 2

z 3

6 K. 0 A 2 A 4 7 3 , 2 4 H

7A, M1(2, 5,3) ,

M1M0 = ( 1, 3, 2) . 27IH A A

7A l 7 27 7

s = (2, 3,4) .

0 2 A ,

7H 2 2 6 A 2 (3.33):

uuuuuuur

M1M0 =

= 6i

8 j

9k.

1 3

% A D 7 6 A 2 (3.33):

+ ( 8)2 + ( 9)2

d =

181

22 + ( 3)2 + 42

181

: 7 7A 29 .

8 % ! # 3.3

1.5 'H 2 .

2.0 2 .

3.0 2, A 23 A A.

4.0 2, 7H I

22 23 A 22 A A.

5.0 2, 7H , 2 4 H

7A.

6.0 A 7 7A.

7.% 4 A, H 27 7 'H

7A A A.

8.% 24 2: “ 2 A A 4 7A A

7….. ”.# 2 D 2 7A 7A?

9.% 24 2: “ 2 A A 4 7A 2 3I

7….. ”. # 2 D 2 7A 7A

10.! 2 2 A 4 2 7A. # 2 D 2

7A 2?

11.0 6 A 2 27 4 7 7 7 2.

12.0 6 A 2 27 4 7 7 7 7A.

3.4. #% # 7

% A 0 A A 3 7 2 IH A

•V!! .

•+ ' !.

•" ' !.

% 2 7 A 2 0 A 2 3 27 A

5 3 . % 2 ' 3 7 [2], 2 4, .59-65 2 2 I – A 2 I A 2 4.

A - 6 A ' 7 23 ' Y1 5 3 Y 31-40 A A.

V!!

# ! # 7 2 7 A 4

, 7A 23 A Oxy 2 7I

I :
Ax2 + 2Bxy + Cy2 + Dx + Ey + F = 0,	(3.34)
7 ' A A, B,C 2 27.

% 2 7 A 7I A ' 7

= 23I 4 7 A ,

2 A ' 2 . ' 2

'2 2 7A 7 A I 7

A, 7 2 D A – A

7A. , A A 7 2

V!! 7 2 7 7,

A :

x2	+	y2	= 1	,	(3.35)
a2		b2

a b 2I' 2 4 23 2. " 2 A 6 A D22.

" 7 2, 27 D22 2 7I 7 5 7:

	x2		y2
		, 1		1	\| x \| a,\| y \| b , . .	D22 2 4
	a2		b2
7A 23,					A A	a x a, b y b ( . 3.27).

A 7 D22 7A : c 3I Oy - D

B1(0, b) B2 (0,b) ; 3I Ox - A1( a,0) A2(a,0) . @ I 7

# K D22.				A1 A2 = 2a B1B2 = 2b I 7				' ! K
! D22. ,
2 a b I 7 ' ! K !						y
!&.
% A x y 4 7						b	M
D22		7. @				B2
,		D22		AA
23		Ox	Oy , 4		-a A1			A2	a
23 2 A –					F1	O		F2	x
O ( I			D22);			B1
D A	A A 2 53 3 ,					B1
D A	A A 2 53 3 ,
7	2 4					-b
				99	.	, 3.27

<<< < Предыдущая 1 2 3 4 5 6 7 8 910 / 1210 11 12 > Следующая >>>

Соседние файлы в папке attachments_22-12-2011_21-07-09

#
02.04.2015494.5 Кб10kontrol 1.pdf
#
02.04.2015465.65 Кб10razdel 1.pdf
#
02.04.2015254.75 Кб10razdel 2.pdf
#
02.04.2015467.57 Кб10razdel 3.pdf
#
02.04.2015738.49 Кб11razdel 4.pdf
#
02.04.20151.03 Mб11semestr1_1.pdf
#
02.04.20151.18 Mб9semestr1_2.pdf
#
02.04.2015228.88 Кб16test11.pdf
#
02.04.201586.53 Кб26titul list.pdf