Compute the curl of the following vector field. F = (32? sin y, 3xz? cos y,...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
9. Let V(x,y,+) - +w7+ sin(x + y)e'] + cos(x + 2) be a vector field in R'. Compute the curl and divergence of the vector field.
= Consider the vector field F(x, y) (cos y + y cos x)i + (sin x – xsin y)j. Show whether the function f(x,y) = x COS Y – y sin x is a potential function for the vector field, F.
Consider the vector field (-7.-2.3) xr, where r= = (x,y,z). a. Compute the curl of the field and verify that it has the same direction as the axis of rotation b. Compute the magnitude of the curl of the field. a. The curl of the field is (i+O; Ok b. The magnitude of the curl of the field is (Type an exact answer, using radicals as needed.)
Consider the vector field. F(x, y, z) = (98 sin(y), 4e' sin(z), 2e sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =
Consider the vector field.
F(x, y, z) =
6ex sin(y), 8ey sin(z), 5ez
sin(x)
Consider the vector field. F(x, y, z) = (6e* sin(y), 8ey sin(z), 5e? sin(x)) (a) Find the curl of the vector field. curl F = (-8e'sin(z), – 5e'sin(x), – 6e'sin(y)) x (b) Find the divergence of the vector field. div F = 6e sin(y) + 8e) sin(z) + 5e+sin(x)
F(x,y,z)= (y² +e",2xy +z sin y, -cos y) is a gradient vector field. Compute Sc F. dr where C=C UC2, C, is the curve y=x*, z =0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3).
7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)= e' sin yi+e' cos yj+zk F.de where is the curve of intersection of the plane : = 5 - x and the cylinder rº + y2 = 9. 8. Use Stokes Theorem to evaluate F(x, y, - ) = xyi +2=j+3yk
Find the divergence of the following vector field. F = (4yz sin x, 9xz cos y, xy cos z) The divergence of F is