Answer this question as soon as possible Let K = {(x,y, z) ER: x > 0, 0 < y< -x+ 2, 0< z <2}And F R' R be the vector field defined by->F(x, y, z) = (2x²z – 2xz, -a² xyz, e*y + z?)With o E R The outward flux of F across KO (A) Is positive ifla < 2O (B) is negative for every a>0O (C) is negative if and only if o> 2O (D) vanishes if and only if a= 2

Answered: Let K = {(x,y, z) ER: x >0, 00 O (C) is…

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Let K = {(x,y, z) ER: x >0, 00 O (C) is negative if and only if a > 2 (D) vanishes if and only ifa=2

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Question

Answer this question as soon as possible

Let K = {(x,y, z) ER: x > 0, 0 < y< -x+ 2, 0< z <2}
And F R' R be the vector field defined by
->
F(x, y, z) = (2x²z – 2xz, -a² xyz, e*y + z?)
With o E R The outward flux of F across K
O (A) Is positive ifla < 2
O (B) is negative for every a>0
O (C) is negative if and only if o> 2
O (D) vanishes if and only if a= 2

Expert Solution

Step 1

To calculate the outward flux of the vector field F across the surface S, use the divergence theorem which states that

$∯_{S} F \cdot d S = ∭_{V} (\nabla \cdot F) d V$ .

Step by step

Solved in 4 steps

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