Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r> Use the parametric curve to convert the vector field into a parametric vector field. F() =(- 21, 3r", 1*) B F(1) = (-21, 61, 1) © F() = (-31, 4r", 41²) F(1) = (21, 31, 1') Now find the derivative of the parametric curve. r() = (21, 31, r') B r) = (2. 3, 3r) © r() = (0, 0, 30)> O r(1) = (2. 3, 1) Now that you have found the parametric vector field and the derivative of the parametric curve, you can use them to find the General Line Integral for this situation. General Line Integral for Vector Fields= F(1) - r'(1) di and Intervat: [0, 1] F(1) . r'(1) di = 3.2 |F) -F) dt = 0.733 © Srm F(1) - r'(1) dt = 1.8 F(1) - r'(1) di = 4.766
Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r> Use the parametric curve to convert the vector field into a parametric vector field. F() =(- 21, 3r", 1*) B F(1) = (-21, 61, 1) © F() = (-31, 4r", 41²) F(1) = (21, 31, 1') Now find the derivative of the parametric curve. r() = (21, 31, r') B r) = (2. 3, 3r) © r() = (0, 0, 30)> O r(1) = (2. 3, 1) Now that you have found the parametric vector field and the derivative of the parametric curve, you can use them to find the General Line Integral for this situation. General Line Integral for Vector Fields= F(1) - r'(1) di and Intervat: [0, 1] F(1) . r'(1) di = 3.2 |F) -F) dt = 0.733 © Srm F(1) - r'(1) dt = 1.8 F(1) - r'(1) di = 4.766
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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We are given a
![Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r>
Use the parametric curve to convert the vector field into a parametric vector field.
F() =(- 21, 3r", 1*)
B F(1) = (-21, 61, 1)
© F() = (-31, 4r", 41²)
F(1) = (21, 31, 1')
Now find the derivative of the parametric curve.
r() = (21, 31, r')
B r) = (2. 3, 3r)
© r() = (0, 0, 30)>
O r(1) = (2. 3, 1)
Now that you have found the parametric vector field and the derivative of the parametric curve, you can use them to find the
General Line Integral for this situation.
General Line Integral for Vector Fields=
F(1) - r'(1) di and Intervat: [0, 1]
F(1) . r'(1) di = 3.2
|F) -F) dt = 0.733
© Srm
F(1) - r'(1) dt = 1.8
F(1) - r'(1) di = 4.766](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70427613-39b9-414c-b7e6-f1c6a3a1890c%2F6ce1ff1a-13da-425b-958e-fab83814272f%2F1zdnyx2_processed.png&w=3840&q=75)
Transcribed Image Text:Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r>
Use the parametric curve to convert the vector field into a parametric vector field.
F() =(- 21, 3r", 1*)
B F(1) = (-21, 61, 1)
© F() = (-31, 4r", 41²)
F(1) = (21, 31, 1')
Now find the derivative of the parametric curve.
r() = (21, 31, r')
B r) = (2. 3, 3r)
© r() = (0, 0, 30)>
O r(1) = (2. 3, 1)
Now that you have found the parametric vector field and the derivative of the parametric curve, you can use them to find the
General Line Integral for this situation.
General Line Integral for Vector Fields=
F(1) - r'(1) di and Intervat: [0, 1]
F(1) . r'(1) di = 3.2
|F) -F) dt = 0.733
© Srm
F(1) - r'(1) dt = 1.8
F(1) - r'(1) di = 4.766
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