Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = < u cos v, u sin v, v > 0 < u < 3, 0 < v < T with upward orientation.
Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = < u cos v, u sin v, v > 0 < u < 3, 0 < v < T with upward orientation.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.1: Vector In R^n
Problem 27E: Determine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)
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![Evaluate
F.dS,where F = <y, – x, z > and S is the helicoid with vector equation
r(u, v) = < u cos v, u sin v, v > 0 <u < 3, 0 < v< TWwith upward orientation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F984318a6-effd-40bc-9bb3-2207dc222889%2F34715988-112e-403b-b37b-f47064489766%2Ft7bfdn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate
F.dS,where F = <y, – x, z > and S is the helicoid with vector equation
r(u, v) = < u cos v, u sin v, v > 0 <u < 3, 0 < v< TWwith upward orientation.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given that, and where and .
Find as follows.
Therefore, the normal upward vector to the surface is , .
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