Экзамен / Ответы на печатные билеты

2. α = −6.

3. (x − 1)2 + 2(y + 1)2 − 3z2 + 5 = 0 —

.

4. d = 3. 5.

x + 1

=

y − 2

=

z

. 6. λ = 1,

e = (1,2),

6

−2

−5

1

1

2.

b = {1;

1

;−

1

}. 3. P(x) = 2p (x)+ 3p (x)+ p

(x). 4. C = −1. 5. 300.

2

2

1

2

3

6.

(x − 1)2 + (y + 5)2 + (z − 2)2 = 36,

1.

3

2. 129. 3. x = {1,2,3}. 4.

,

(2,1,0).

5. x = 2, y = 2t − 1, z = −t + 3. 6. T

4

3

−1AT =

.

−17

−13

4

2. a = {1,−1,±

1

. 4. λ = 2,

= (3,1), λ = 7, e

= (2,−1).

2}. 3. C =

e

2

3

1

1

2

5. x − 3y + z − 1 = 0. 6.

,

2.

6

2.

6.

3.

0.

4.

(x + 1)2

− (z − 2)2

= 4(y − 2). 5. {−2,4,8}. 6.

.

7

−1

1

3

2.{−85,−35,−40}. 3.

. 4. −

15

(1,−1,2).

. 5.

,

2

3

1

30

6.

x − 1

=

y − 2

=

z − 3

.

2

0

−1

8

2.

{

3,−

3,−

3}.

3.

. 4.

,

(1,−2,−2). 5.

.

9

2.

{45,18,−1}.

3.

arccos

34

. 4.

.

39

0

0

0

−1

5.

0

0

. 6. x − 2z − 4 = 0.

0

1

0

2.

450. 3. 5. 4.

8

. 5. λ = 5,

e = (4,3),

λ = −2, e

= (1,−1).

14

1

1

2

2

6.

x − 3

=

y − 1

=

z

.

2

1

1

11

2.

6

14. 3. A = 1. 4. a = −4. 5. 2x + 3y + z = 0. 6. e3

= (6,5,3).

12

2.

{−1,5,4}. 3.

a > −4. 4.

20x − 4y − 5z + 133 = 0

2

−1

−1

20x − 4y − 5z − 119 =

0. 5. {−4,10,−2}

1

−1

−1

. 6.

2

.

3

−1

−1

2

2.

cosα =

4

,

cosβ =

3

,

cosγ = 0.

3.

C = −6.

4. x2 − 4y2 − 4z2 − 4x + 4 = 0.

5.

.

6.

y + z + 1 = 0.

14

2.

27. 3.

(z − 1)2 − 4y2 = 4(x − 3).

2.

,

(1,−1,2). 3. −

16

.

3

−1

0

0

x − 1

z + 2

−1

=

y

=

4.

2

0

. 5.

. 6.

7.

3

4

1

1

−1

3

2.

97. 3. λ = λ = −1, e = (1,1). 4.

5

. 5. B = -4,

C = 0. 6. 3.

1

2

3

18

2.

x + y + 1 = 0. 3.

x − 1

=

y − 1

=

z

.

4.

α = -1, β = -9.

11

1

−7

5.

,

(1,0,1). 6.

0

1

1

0

,

2.

2 13.

3. λ1 = 4, e1 = (2,5),

λ2

= −3, e2 = (1,−1).

4. a < −8.

5.

1089. 6. A = 3, B = 6.

20

2. 3. 3.

. 4. −

8

. 5. A = 1. 6. a < 3.

2

21

21

2.

AB = 3,

AC = 3, BC =

.

3.

{−1,−1,2}. 4. 1. 5.

arcsin

20

.

26

21

6.

a ¹ 1.

22

2.

x + 1

=

y + 1

=

z + 1

. 3.

−2. 4. (0,−1). 5. a = −1, b = −4, c = −1.

2

1

0

6.

−3,

,

.

23

2.

x = 2t + 1,

y = 5t − 3, z = −t − 1. 3. {−21,−49,−7}. 4.

7

. 5. a > 4.

18

24

1

2. A = 4, B = −6. 3. {±2;−2; 2

1

3

2}. 4.

. 5.

,

−1

2

3