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with an arrow the direction in which t increases. 7. r(t) = (sin t, t) 9. r(t) = (t, 2 t, 2t) 11. r(t) = (3, t, 2 - t²) - 8. r(t) = (t²-1, t) 10. r(t) = (sin πt, t, cos mt) 12. r(t) = 2 cos ti + 2 sin tj + k 13. r(t) = t¹i + t'j + tºk 14. r(t) = cos ti - cos tj + sin t k 15-16 Draw the projections of the curve on the three coordinate Was the ong to help sketch the curve

with an arrow the direction in which t increases. 7. r(t) = (sin t, t) 9. r(t) = (t, 2 t, 2t) 11. r(t) = (3, t, 2 - t²) - 8. r(t) = (t²-1, t) 10. r(t) = (sin πt, t, cos mt) 12. r(t) = 2 cos ti + 2 sin tj + k 13. r(t) = t¹i + t'j + tºk 14. r(t) = cos ti - cos tj + sin t k 15-16 Draw the projections of the curve on the three coordinate Was the ong to help sketch the curve

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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2t³ - 1 7-14 Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. 7. r(t) = (sin t, t) 9. r(t) = (t, 2 t, 2t) 11. r(t) = (3, t, 2 - t²) 12. r(t) = 2 cos ti + 2 sin tj + k 13. r(t) = t¹i + tªj + tºk 14. r(t) = cos ti - cos tj + sin t k 8. r(t) = (t²-1, t) 10. r(t) = (sin Tt, t, cos nt) 15-16 Draw the projections of the curve on the three coordinate planes. Use these projections to help sketch the curve. 15. r(t) = (t, sin t, 2 cos t) 16. r(t) = (t, t, t²) 17-20 Find a vector equation and parametric equations for the line segment that joins P to Q. 17. P(2, 0, 0), Q(6, 2,-2) 19. P(0, -1, 1), (1,3,4) I 21-26 Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices. II y 18. P(-1, 2, -2), Q(-3, 5, 1) 20. P(a, b, c), Q(u, v, w) ZA 155 25. 26. 27. 28. 29. 30. 31. 32. 33- equ poi 33. 34. 35. 36. 37. 38.
Transcribed Image Text:2t³ - 1 7-14 Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. 7. r(t) = (sin t, t) 9. r(t) = (t, 2 t, 2t) 11. r(t) = (3, t, 2 - t²) 12. r(t) = 2 cos ti + 2 sin tj + k 13. r(t) = t¹i + tªj + tºk 14. r(t) = cos ti - cos tj + sin t k 8. r(t) = (t²-1, t) 10. r(t) = (sin Tt, t, cos nt) 15-16 Draw the projections of the curve on the three coordinate planes. Use these projections to help sketch the curve. 15. r(t) = (t, sin t, 2 cos t) 16. r(t) = (t, t, t²) 17-20 Find a vector equation and parametric equations for the line segment that joins P to Q. 17. P(2, 0, 0), Q(6, 2,-2) 19. P(0, -1, 1), (1,3,4) I 21-26 Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices. II y 18. P(-1, 2, -2), Q(-3, 5, 1) 20. P(a, b, c), Q(u, v, w) ZA 155 25. 26. 27. 28. 29. 30. 31. 32. 33- equ poi 33. 34. 35. 36. 37. 38.
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