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For the vector function G(t) = -3cos(2t) i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (d) Gx dt (a) G•G - dt (Hint. The answer for part (d) can be deduced from parts (a), (b) and (c). What does your answer in part (c) tell you?)

For the vector function G(t) = -3cos(2t) i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (d) Gx dt (a) G•G - dt (Hint. The answer for part (d) can be deduced from parts (a), (b) and (c). What does your answer in part (c) tell you?)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 1AEXP
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hello i have the solutions, however i am unable to understand anything at all. i have no prior knowledge to this, is it possible to explain this in depth to me thanks !

1. For the vector function G(t) = -3cos(2t)i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (a) G•G (d) - dt dt (Hint. The answer for part (d) can be deduced from parts (a), (b) and (c). What does your answer in part (c) tell you?) (Solution) (a) G•G=|G| = 9 cos (2t) +9 sin² (2t) +1² = 10. %3D dG = 6 sin(2t) i+6 cos(2t) j dt (b) dG 12 dG 36sin? dt dG = 36 sin (21) + 36 cos (20) = 36. dt dt (c) G• dG = [-3cos(2t), 3sin(2t), 1] • [6sin(2t), 6 cos(2t), 0] = 0. dt (d) From part (c), we know that Gand (dG / dt) are perpendicular to each other. Now Gx (dG/ dt)|=G||× (dG / dt)||sin(90°)|= 6/10 (after using the answers in parts (a) and (b)).
Transcribed Image Text:1. For the vector function G(t) = -3cos(2t)i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (a) G•G (d) - dt dt (Hint. The answer for part (d) can be deduced from parts (a), (b) and (c). What does your answer in part (c) tell you?) (Solution) (a) G•G=|G| = 9 cos (2t) +9 sin² (2t) +1² = 10. %3D dG = 6 sin(2t) i+6 cos(2t) j dt (b) dG 12 dG 36sin? dt dG = 36 sin (21) + 36 cos (20) = 36. dt dt (c) G• dG = [-3cos(2t), 3sin(2t), 1] • [6sin(2t), 6 cos(2t), 0] = 0. dt (d) From part (c), we know that Gand (dG / dt) are perpendicular to each other. Now Gx (dG/ dt)|=G||× (dG / dt)||sin(90°)|= 6/10 (after using the answers in parts (a) and (b)).
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