1.18. x = {8,

1,

2} ,

p = {1,

2,

−1} ,

q = {3,

0,

2} ,

r =

{−1,

1,

1}.

1.19. x = {−9,

−8,

−3} ,

p = {1,

4,

1} ,

q = {−3,

2,

0} ,

r = {1,

−1, 2}.

1.20. x = {−5,

9,

−13} ,

p = {0,

1,

−2}

,

q = {3,

−1,

1} ,

r = {4,

1,

0}.

1.21. x = {−15,

5,

6} ,

p = {0,

5,

1} ,

q = {3,

2,

−1} ,

r = {−1,

1,

0}.

1.22. x = {8,

9,

4} ,

p = {1,

0,

1}

,

q = {0,

−2,

1} ,

r = {1,

3,

0}.

1.23. x = {23,

−14,

−30} ,

p = {2,

1,

0} ,

q = {1,

−1,

0} ,

r = {−3,

2,

5}.

1.24. x = {3,

1,

3} ,

p = {2,

1,

0} ,

q = {1,

0,

1} ,

r = {4,

2,

1}.

1.25. x = {−1,

7,

0} ,

p = {0,

3,

1} ,

q = {1,

−1,

2} ,

r = {2,

−1,

0}.

1.26. x = {11,

−1,

4} ,

p = {1,

−1,

2} ,

q = {3,

2,

0} ,

r = {−1,

1,

1}.

1.27. x = {−13,

2,

18} ,

p = {1,

1,

4} ,

q = {−3,

0,

2}

,

r = {1,

2, −1}.

1.28. x = {0,

−8, 9} ,

p = {0,

−2,

1} ,

q = {3,

1,

−1} ,

r = {4,

0,

1}.

1.29. x = {8,

−7, −13} ,

p = {0,

1,

5} ,

q = {3,

−1,

2} ,

r = {−1,

0,

1}.

1.30. x = {2,

7,

5} ,

p = {1,

0,

1} ,

q = {1,

−2,

0} ,

r =

{0,

3,

1}.

1.31. x = {15,

−20,

−1} , p = {0,

2,

1} ,

q = {0,

1,

−1} ,

r = {5,

−3, 2}.

Задача 2. Коллинеарны ли векторы c1 и c2 , построенные по векторам a и b?

2.1. a = {1,

−2,

3} ,

b = {3,

0,

−1} ,

c1 = 2a + 4b,

c2 = 3b − a.

2.2. a = {1,

0,

1} ,

b = {−2,

3,

5} ,

c1 = a + 2b,

c2

= 3a − b.

2.3. a = {−2,

4,

1} ,

b = {1,

−2,

7} ,

c1 = 5a + 3b,

c2

= 2a − b.

2.4. a = {1,

2,

−3} ,

b = {2,

−1,

−1} ,

c1 = 4a + 3b,

c2

= 8a − b.

2.5. a = {3,

5,

4} ,

b = {5,

9,

7} , c1 = −2a + b,

c2 = 3a − 2b.

2.6. a = {1,

4,

−2} ,

b = {1,

1,

−1} ,

c1 = a + b,

c2

= 4a + 2b.

2.7. a = {1,

−2,

5} ,

b = {3,

−1,

0} ,

c1 = 4a − 2b,

c2 = b − 2a.

2.8. a = {3,

4,

−1} ,

b = {2,

−1,

1} ,

c1 = 6a − 3b,

c2

= b − 2a.

224

2.9. a = {−2,

−3,

−2} ,

b = {1,

0,

5} ,

c1 = 3a + 9b,

c2

= −a − 3b.

2.10. a = {−1,

4,

2} ,

b = {3,

−2,

6} ,

c1 = 2a − b,

c2

= 3b − 6a.

2.11. a = {5,

0,

−1} ,

b = {7,

2,

3} ,

c1 = 2a − b,

c2 = 3b − 6a.

2.12. a = {0,

3,

−2} ,

b = {1,

−2,

1} ,

c1 = 5a − 2b,

c2

= 3a + 5b.

2.13. a = {−2,

7,

−1} ,

b = {−3,

5,

2} ,

c1 = 2a + 3b,

c2 = 3a + 2b.

2.14. a = {3,

7,

0} ,

b = {1,

−3,

4}

,

c1 = 4a − 2b,

c2

= b − 2a.

2.15. a = {−1,

2,

−1}

,

b = {2,

−7,

1}

,

c1 = 6a − 2b,

c2 = b − 3a.

2.16. a = {7,

9,

−2} ,

b = {5,

4,

3} ,

c1 = 4a − b,

c2 = 4b − a.

2.17. a = {5,

0,

−2} ,

b = {6,

4,

3} ,

c1 = 5a − 3b,

c2

= 6b −10a.

2.18. a = {8,

3,

−1} ,

b = {4,

1,

3} ,

c1 = 2a − b,

c2 = 2b − 4a.

2.19. a = {3,

−1,

6} ,

b = {5,

7,

10} ,

c1 = 4a − 2b,

c2

= b − 2a.

2.20. a = {1,

−2,

4} ,

b = {7,

3,

5} ,

c1 = 6a − 3b,

c2

= b − 2a.

2.21. a = {3,

7,

0} ,

b = {4,

6,

−1} ,

c1 = 3a + 2b,

c2

= 5a − 7b.

2.22. a = {2,

−1,

4} ,

b = {3,

−7,

−6} ,

c1 = 2a − 3b,

c2 = 3a − 2b.

2.23. a = {5,

−1,

−2}

,

b = {6,

0,

7} ,

c1 = 3a − 2b,

c2

= 4b − 6a.

2.24. a = {−9,

5,

3} ,

b = {7,

1,

−2} ,

c1 = 2a − b,

c2

= 3a + 5b.

2.25. a = {4,

2,

9} ,

b = {0,

−1,

3} ,

c1 = 4b − 3a,

c2

= 4a − 3b.

2.26. a = {2,

−1,

6} ,

b = {−1,

3,

8} ,

c1 = 5a − 2b,

c2

= 2a − 5b.

2.27. a = {5,

0,

8} ,

b = {−3,

1,

7} ,

c1 = 3a − 4b,

c2

=12b − 9a.

2.28. a = {−1,

3,

4} ,

b = {2,

−1,

0} ,

c1 = 6a − 2b,

c2

= b − 3a.

2.29. a = {4,

2,

−7} ,

b = {5,

0,

−3} ,

c1 = a − 3b,

c2

= 6b − 2a.

2.30. a = {2,

0,

−5} ,

b = {1,

−3,

4} ,

c1 = 2a − 5b,

c2

= 5a − 2b.

2.31. a = {−1,

2,

8} ,

b = {3,

7,

−1} ,

c1 = 4a − 3b,

c2

= 9b −12a.

225