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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)).

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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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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