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Question 6 A vector field is given by F(r) = zi+a+yk, and a paraboloid is given by S = {(x, y, z) € R³ |z=1-a²-y², z [0, 1]}, as shown in Figure 6. Figure 6 i) Compute the parametric line integral W = F(r(t)). d) dt. dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)i + sin(t))+0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with [[ (V x F). ñ ds. M main.

Question 6 A vector field is given by F(r) = zi+a+yk, and a paraboloid is given by S = {(x, y, z) € R³ |z=1-a²-y², z [0, 1]}, as shown in Figure 6. Figure 6 i) Compute the parametric line integral W = F(r(t)). d) dt. dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)i + sin(t))+0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with [[ (V x F). ñ ds. M main.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Question 6 A vector field is given by F(r) = z2+3+ yk, and a paraboloid is given by S = {(x, y, z) = R³ |z=1-2² - y², z € [0, 1]}, as shown in Figure 6. 1 Figure 6 i) Compute the parametric line integral W = F(r(t)). dt. dr(t) dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)2 + sin(t)j +0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with (V x F). ñ ds. 7x Mar
Transcribed Image Text:Question 6 A vector field is given by F(r) = z2+3+ yk, and a paraboloid is given by S = {(x, y, z) = R³ |z=1-2² - y², z € [0, 1]}, as shown in Figure 6. 1 Figure 6 i) Compute the parametric line integral W = F(r(t)). dt. dr(t) dt C is the counter-clockwise circular boundary of S in the ry-plane, with para- metric definition r(t) = cos(t)2 + sin(t)j +0k, t€ [0,2m). ii) Compute the curl of F; i.e. Vx F. iii) Confirm your answer for W with (V x F). ñ ds. 7x Mar
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