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In Problems 1-6, find a vector equation for the line through the given points. 1. (1, 2, 1), (3, 5, -2) 3. (½, −1, 1), (−3, 1, − 1) 5. (1, 1, −1), (−4, 1, −1) In Problems 7-12, find parametric equations for the line through the given points. 7. (2, 3, 5), (6, -1, 8) 9. (1, 0, 0), (3, -2, -7) 11. (4, ½, 3), (−6, — ½, ½) 2. (0, 4, 5), (−2, 6, 3) 4. (10, 2, 10), (5, −3, 5) 6. (3, 2, 1), (§, 1, -2) 13. (1, 4, −9), (10, 14, -2) 15. (4, 2, 1), (-7, 2, 5) 17. (5, 10, −2), (5, 1, −14) 8. (2, 0, 0), (0, 4, 9) 10. (0, 0, 5), (2, 4, 0) 12. (-3, 7, 9), (4, −8, −1) In Problems 13-18, find symmetric equations for the line through the given points. 14. (3, 0, −½), (1, 3, 4) 16. (-5, -2, -4), (1, 1, 2) 18. (§,−1, §), (3, 3, - 10) In Problems 19-22, find parametric and symmetric equations for the line through the given point parallel to the given vector. 19. (4, 6, -7), a = (3, ½, -³/) 20. (1, 8, -2), a = -7i - 8j 21. (0, 0, 0), a = 5i + 9j + 4k 22. (0, -3, 10), a = (12, -5, -6)

In Problems 1-6, find a vector equation for the line through the given points. 1. (1, 2, 1), (3, 5, -2) 3. (½, −1, 1), (−3, 1, − 1) 5. (1, 1, −1), (−4, 1, −1) In Problems 7-12, find parametric equations for the line through the given points. 7. (2, 3, 5), (6, -1, 8) 9. (1, 0, 0), (3, -2, -7) 11. (4, ½, 3), (−6, — ½, ½) 2. (0, 4, 5), (−2, 6, 3) 4. (10, 2, 10), (5, −3, 5) 6. (3, 2, 1), (§, 1, -2) 13. (1, 4, −9), (10, 14, -2) 15. (4, 2, 1), (-7, 2, 5) 17. (5, 10, −2), (5, 1, −14) 8. (2, 0, 0), (0, 4, 9) 10. (0, 0, 5), (2, 4, 0) 12. (-3, 7, 9), (4, −8, −1) In Problems 13-18, find symmetric equations for the line through the given points. 14. (3, 0, −½), (1, 3, 4) 16. (-5, -2, -4), (1, 1, 2) 18. (§,−1, §), (3, 3, - 10) In Problems 19-22, find parametric and symmetric equations for the line through the given point parallel to the given vector. 19. (4, 6, -7), a = (3, ½, -³/) 20. (1, 8, -2), a = -7i - 8j 21. (0, 0, 0), a = 5i + 9j + 4k 22. (0, -3, 10), a = (12, -5, -6)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Problems 1-6, find a vector equation for the line through the given points. 1. (1, 2, 1), (3, 5, −2) 2. (0, 4, 5), (−2, 6, 3) 3. (½, −½, 1), (−½, ½, −½) 2 4. (10, 2, 10), (5, −3, 5) 5. (1, 1, −1), (−4, 1, −1) 6. (3, 2, 1), (§, 1, −2) In Problems 7-12, find parametric equations for the line through the given points. 7. (2, 3, 5), (6, -1, 8) 9. (1, 0, 0), (3, —2, −7) 11. (4, ½, 3), (−6, – ½, ½) 8. (2, 0, 0), (0, 4, 9) 10. (0, 0, 5), (-2, 4, 0) 12. (-3, 7, 9), (4, −8, −1) In Problems 13–18, find symmetric equations for the line through the given points. 13. (1, 4, −9), (10, 14, −2) 15. (4, 2, 1), (-7, 2, 5) 17. (5, 10, −2), (5,1,−14) 14. (3, 0, −¹), (1, 3, 4) 16. (-5, -2,-4), (1, 1, 2) 18. (§, 18. (§, −1, §), (§⁄, §, -1) In Problems 19-22, find parametric and symmetric equations for the line through the given point parallel to the given vector. 19. (4, 6, -7), a = (3, ½, − ³) 20. (1,8, -2), a = −7i - 8j 21. (0, 0, 0), a = 5i + 9j + 4k 22. (0, −3, 10), a = (12, −5, −6)
Transcribed Image Text:In Problems 1-6, find a vector equation for the line through the given points. 1. (1, 2, 1), (3, 5, −2) 2. (0, 4, 5), (−2, 6, 3) 3. (½, −½, 1), (−½, ½, −½) 2 4. (10, 2, 10), (5, −3, 5) 5. (1, 1, −1), (−4, 1, −1) 6. (3, 2, 1), (§, 1, −2) In Problems 7-12, find parametric equations for the line through the given points. 7. (2, 3, 5), (6, -1, 8) 9. (1, 0, 0), (3, —2, −7) 11. (4, ½, 3), (−6, – ½, ½) 8. (2, 0, 0), (0, 4, 9) 10. (0, 0, 5), (-2, 4, 0) 12. (-3, 7, 9), (4, −8, −1) In Problems 13–18, find symmetric equations for the line through the given points. 13. (1, 4, −9), (10, 14, −2) 15. (4, 2, 1), (-7, 2, 5) 17. (5, 10, −2), (5,1,−14) 14. (3, 0, −¹), (1, 3, 4) 16. (-5, -2,-4), (1, 1, 2) 18. (§, 18. (§, −1, §), (§⁄, §, -1) In Problems 19-22, find parametric and symmetric equations for the line through the given point parallel to the given vector. 19. (4, 6, -7), a = (3, ½, − ³) 20. (1,8, -2), a = −7i - 8j 21. (0, 0, 0), a = 5i + 9j + 4k 22. (0, −3, 10), a = (12, −5, −6)
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