Question

Use the surface integral in Stokes' theorem to calculate the circulation of the vector field 𝐹̅ (𝑥, 𝑦, 𝑧) = <−3𝑧, 𝑦^2, 2𝑦> around the curve C – the intersection of the cylinder 𝑥^2 + 𝑦^2 = 4 and the plane 𝑥 − 3𝑦 − 2𝑧 = 1, in the counterclockwise direction if viewing from above.

Name: use the surface integral in stokes theorem to calculate the circulation of the vector field f x y z 3z y2 2y around the curve c the intersection of the cylinder x2 y2 4 and the plane x 3y 2z 03336
Uploaded: 2020-05-11T14:53:12-08:00
Duration: 3 min 50 s
Channel: Vikash Ranjan
Description: use the surface integral in stokes theorem to calculate the circulation of the vector field f x y z 3z y2 2y around the curve c the intersection of the cylinder x2 y2 4 and the plane x 3y 2z 03336

          Use the surface integral in Stokes' theorem to calculate the circulation of the vector field 𝐹̅ (𝑥, 𝑦, 𝑧) = <−3𝑧, 𝑦^2, 2𝑦> around the curve C – the intersection of the cylinder 𝑥^2 + 𝑦^2 = 4 and the plane 𝑥 − 3𝑦 − 2𝑧 = 1, in the counterclockwise direction if viewing from above.

Added by Amanda J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vikash Ranjan

05/11/2020

Step 1

To use Stokes' theorem, we need to find the normal vector to the surface. The surface is defined by the intersection of the cylinder 𝑥^2 + 𝑦^2 = 4 and the plane 𝑥 − 3𝑦 − 2𝑧 = 1. To find the normal vector, we can take the gradient of the equation of the surface. Show more…

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Use the surface integral in Stokes' theorem to calculate the circulation of the vector field 𝐹̅ (𝑥, 𝑦, 𝑧) = <−3𝑧, 𝑦^2, 2𝑦> around the curve C – the intersection of the cylinder 𝑥^2 + 𝑦^2 = 4 and the plane 𝑥 − 3𝑦 − 2𝑧 = 1, in the counterclockwise direction if viewing from above.