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3. Find the work of the vector field F(2, y, ) = yi along the curve which is obtained as the intersection of the surfaces z = a+y-6 and Ga +12y +6. Hint: you may find it useful to complete the squares and use the identity sint = (1- cos(2t)).

3. Find the work of the vector field F(2, y, ) = yi along the curve which is obtained as the intersection of the surfaces z = a+y-6 and Ga +12y +6. Hint: you may find it useful to complete the squares and use the identity sint = (1- cos(2t)).

Algebra and Trigonometry (MindTap Course List)
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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Please answer question 3 only.
1:19 Y G D • a A * * 74%i 1. True/False: The vector field F = yzi +xzj + xyk is the gradient field of some diferentiable function f(x, y, 2). (Justify your answer.) 2. True/False: The vector field G = ri +a*j is not the gradient field of any funet ion g(x, y) whose second order derivatives are continuous over R. (Just ify your answer.) 3. Find the work of the vector field F(r, y, 2) = yi along the curve which is obtained as the intersection of the surfaces = a+y-6 and 6a+12y = 2+6. Hint: you may find it useful to complete the squares and use the identity sin?t = (1- cos(2t)). II
Transcribed Image Text:1:19 Y G D • a A * * 74%i 1. True/False: The vector field F = yzi +xzj + xyk is the gradient field of some diferentiable function f(x, y, 2). (Justify your answer.) 2. True/False: The vector field G = ri +a*j is not the gradient field of any funet ion g(x, y) whose second order derivatives are continuous over R. (Just ify your answer.) 3. Find the work of the vector field F(r, y, 2) = yi along the curve which is obtained as the intersection of the surfaces = a+y-6 and 6a+12y = 2+6. Hint: you may find it useful to complete the squares and use the identity sin?t = (1- cos(2t)). II
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