Let F₁ (x, y, z) = (y, x-z²+2, -2yz) and F₂(x, y, z) = (x − z², -y +2, 2yz). (a) Find the curl of each vector field. (b) Which of these two vector fields is conservative? Find a potential function for the one that is. (c) Let F be either F₁ or F2 (whichever you want), and let C denote the curve shown in the figure which starts at the point (0, 1, 0), stays above the circle x² + y² = 1 and spirals upwards in a clockwise direction to the point (0, 1, 1). Find the exact value of the line integral: Jo F. dr.

Let F₁ (x, y, z) = (y, x-z²+2, -2yz) and F₂(x, y, z) = (x − z², -y +2, 2yz). (a) Find the curl of each vector field. (b) Which of these two vector fields is conservative? Find a potential function for the one that is. (c) Let F be either F₁ or F2 (whichever you want), and let C denote the curve shown in the figure which starts at the point (0, 1, 0), stays above the circle x² + y² = 1 and spirals upwards in a clockwise direction to the point (0, 1, 1). Find the exact value of the line integral: Jo F. dr.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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