8. For the vector field F= 2(x+y) -ŷ 2x² + 2xy,evaluate fF.ds where S is the upper hemisphereevaluate f (VxF) ds whereof x² + y² +2²=1, andS is the upper hemisphereof x² + y² + 2² = 1.SZ

Answered: Image /qna-images/answer/93ed8a9d-0584-4e80-a097-5e90f7d19a0f.jpg

Answered: 3.For the vector field F = 2(x + y) - 9…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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10. Let the vector v = 2i -3j + k, and the vector w = -i+ 3j + 2k. Find v x w.
I'm not too sure how to calculate vector fields
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(13.) Determine whether the vectors span the vector space. (a.) Let u = 2-5t+6t²-t³,v=3+2t-4t² (b.) Let vectors of P3(t). 1 2i -=(²²). -- (28) V= 5 i U= vectors of M2x2(C) over R. (c.) Let u = (2,0), v = (i, 1), w = (0, 2i), y = (1, 1) be the vectors of C² over R.
Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) = = ( Note: Y 2 (x² + y² +2²)³/²¹ (x² + y² + x2)³/²¹ (x² + y² + x2)³/2 • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx = x². Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {Ax, Ay, Az} . Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. • If you need to enter O, enter it in three components, as (0, 0, 0) or {0,0,0}. V x V = ▼ xr= vx= (2A, 2A, 2A₂).

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3.For the vector field F = 2(x + y) - 9 2x² + 2xy, › evaluate fF.ds where S is the upper hemisphere evaluate f (VxF) ds where of x² + y² +2²=1, and S is the upper hemisphere of x² + y² +2²=1. S y