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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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