Consider the vector fieldF = 2i+yj + (x + 2) kand the surface S defined as the surface of a cubewith side length 3 centred at the origin.Use the divergence theorem to calculate the flux of Fover the surface S, i.e.[F.ds.Enter this value in the box below (rounded to twodecimal places if necessary).Answer:

Answered: Image /qna-images/answer/00b97441-94e4-4bee-9afa-b3a05ff8114a.jpg

Answered: Consider the vector field F = 2i+yj +…

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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Let I be the flux of G = (4e³,9x³ex⁹, 0) through the upper hemisphere S of the unit sphere. (a) Find a vector field A such that curl(A) = G. (b) Calculate the circulation of A around as. (c) Compute I, the flux of G through S. (a) A = (b) √ A · ds = (c) I =
Show that if F = xi+yj + zk, then VXF=0. The curl of a vector field F = Mi+Nj + Pk is as follows. ap ƏN ?M ap dy dz dz ?x Use the formula above to find the curl of F=xi+yj + zk. curl F = VXF= VxF = V x (xi+yj+zk) dz dy = - i+ dy dz = i+ İ+ dx dz dz ?x + k j+ dy ax ?x ду ƏN ax k ƏM ду
For the vector field F and curve C, complete the following. a. Determine the points (if any) on the curve C at which the vector field F is tangent to C. b. Determine the points (if any) on the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. where C = = {(x,y): y - 3x² = -4} F= a. Where is F tangent to C? Select the correct choice below and fill in any answer boxes within your choice. OA. F is tangent to C at (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no points where F is tangent to C. OC. F is tangent to C at every point on C.
I need the answer as soon as possible
Find the co-ordinate on the space curve given by the position vector r(t) 5 sin(2t)i +5 cos(2t)j + 24tk, which is at a distance of 267 units along the space curve from the co-ordinate (0,5,0).
In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (X2+y²)k a. State whether F is conservative, and give a one-sentence justification for your statement b. Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation x=at, y=bt, z=ct (0sts1). c. Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.
We consider the vector field F = (xy², -x²y). Let C be the parabola y = x² from the point (-1, 1) to the point (1,1). Find the work exerted by this force along the curve C.

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