For each of the following vector fields, find its curl and determine if it is a gradient field.
For each of the following vector fields, find its curl and determine if it is a...
#5 with all the steps in a clear way please!! In Exercises 3-10, compute the curl of the vector field. 3. = 3x7 – 5zj + yk 4. F = (x2 - y2)ī + 2xyſ 5. F = (-- + y)i + (y+z)+ (-2+ x)k 6. F = 2yzi + 3xz] + Tryk 7. Ě = 221 + 137 + 24K 8. F = "7 + cos yj te- 9. F = (x + yz)i + (y + rzy)j +...
How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
a) Find the length of the curve traced by the given vector function on the indicated interval: r(t)e' costie' sin tj+e'k 0<t<In2 b) Find the gradient of the scalar function f 6xyz + 2x+ xz at (1, 1, -1) c) Find the curl of the given vector field: F(x, y,z) 4xyi + (2x2 +2yz)j+(3z2+y2)k
Consider the given vector field. F(x, y, z) = (9 / sqrt(x2 + y2 + z2)) (x i + y j + z k) Find the curl of the vector field. Then find Divergence
(1 point) (a) Show that each of the vector fields F-4yi + 4x j, G-i ЗУ x2+y2 x?+yi J, and j are gradient vector fields on some domain (not necessarily the whole plane) x2+y2 by finding a potential function for each. For F, a potential function is f(x, y) - For G, a potential function is g(x, y) - For H, a potential function is h(x, y) (b) Find the line integrals of F, G, H around the curve C...
4. (16 points) Determine which of the following vector fields is conservative, and construct a potential function for that field. (iii) H(x, y, z) = (y2 +22,22 + 1, 2yz)
1. (20 points) Identify if the following vector fields are conservative. If there exists a vector field that is conservative, you must also find a potential function for that field. (a) F(x,y,z) = (x3 – xy +z)i + 2 (b) F(x,y,z) = (y+z)i + (x+z)j + (x+y)k (& +y +y-22) i + (- y2)k
1.) (8 pts.) Consider the vector field F(t, y, z) = (3cʻz + 3 + yzbi – (22 - 12)ī + (23 – 2yz +2 + xy)k Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible.
Problem 6 Using Stokes' Theorem, we equate F dr curl F dA. Find curl F- PreviousS us Problem ListNext Noting that the surface is given by (1 point) Calculate the circulation, Fdr7in z - 16-x2 - y2, find two ways, directly and using Stokes' Theorem. dA The vector field F = 6y1-6y and C is the boundary of S, the part of the surface dy dx With R giving the region in the xy-plane enclosed by the surface, this gives...