Need help with Q2. Thank you.Let F be the vector field (x2z, xyz, x2y), and S the paraboloid z = 1 − x2 − y2, z ≥ 0 with upward pointing normal vector.1. Calculate the curl of F, ∇ × F. 2. Calculate (∇ × F) · dS. Problem 1. Let F be the vector field (xz, xyz, x²y), and S the paraboloid z = 1– x² – y²,z > 0 with upward pointing normal vector.1. Calculate the curl of F, V × F.2. Calculate(V x F) · dS.

Answered: Image /qna-images/answer/996776a0-3b61-4776-a52f-07ea0e3fffbe.jpg

Problem 1. Let F be the vector field (x²z, xyz, x²y), and S the paraboloid z = 1 – x² – y², z 2 0 with upward pointing normal vector. 1. Calculate the curl of F, V × F. 2. Calculate (V × F) · dS. S

Problem 1. Let F be the vector field (x²z, xyz, x²y), and S the paraboloid z = 1 – x² – y², z 2 0 with upward pointing normal vector. 1. Calculate the curl of F, V × F. 2. Calculate (V × F) · dS. S

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 12P

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Question

Need help with Q2. Thank you.

Let F be the vector field (x2z, xyz, x2y), and S the paraboloid z = 1 − x2 − y2, z ≥ 0 with upward pointing normal vector.

1. Calculate the curl of F, ∇ × F.

2. Calculate (∇ × F) · dS.

Problem 1. Let F be the vector field (xz, xyz, x²y), and S the paraboloid z = 1– x² – y²,
z > 0 with upward pointing normal vector.
1. Calculate the curl of F, V × F.
2. Calculate
(V x F) · dS.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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