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3. Let P be the curve that follows the helix r(t) = ( cos t sin t from (1, 0, 0) to t/T (1, 0, 2), then follows a great circle of the sphere x² + y²+z² = 5 to the point (1,2,0), and then goes in a straight line to the point (1, 1, 7/2). Find f, F. dr, where F (x, y, z) = yz cos(xyz) xz cos(xyz) xy cos(xyz)

3. Let P be the curve that follows the helix r(t) = ( cos t sin t from (1, 0, 0) to t/T (1, 0, 2), then follows a great circle of the sphere x² + y²+z² = 5 to the point (1,2,0), and then goes in a straight line to the point (1, 1, 7/2). Find f, F. dr, where F (x, y, z) = yz cos(xyz) xz cos(xyz) xy cos(xyz)

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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3. Let \( P \) be the curve that follows the helix \(\vec{r}(t) = \left( \begin{array}{c} \cos t \\ \sin t \\ t/\pi \end{array} \right)\) from \((1, 0, 0)\) to \((1, 0, 2)\), then follows a great circle of the sphere \(x^2 + y^2 + z^2 = 5\) to the point \((1, 2, 0)\), and then goes in a straight line to the point \((1, 1, \pi/2)\). Find \(\int_P \vec{F} \cdot d\vec{r}\), where \(\vec{F}(x, y, z) = \left( \begin{array}{c} yz \cos(xyz) \\ xz \cos(xyz) \\ xy \cos(xyz) \end{array} \right)\).
Transcribed Image Text:3. Let \( P \) be the curve that follows the helix \(\vec{r}(t) = \left( \begin{array}{c} \cos t \\ \sin t \\ t/\pi \end{array} \right)\) from \((1, 0, 0)\) to \((1, 0, 2)\), then follows a great circle of the sphere \(x^2 + y^2 + z^2 = 5\) to the point \((1, 2, 0)\), and then goes in a straight line to the point \((1, 1, \pi/2)\). Find \(\int_P \vec{F} \cdot d\vec{r}\), where \(\vec{F}(x, y, z) = \left( \begin{array}{c} yz \cos(xyz) \\ xz \cos(xyz) \\ xy \cos(xyz) \end{array} \right)\).
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