92. Suppose F(x, y, z) (xyz,x2,zy3) describes the velocity field of a flowing fluid a) Show that F is not a conservative vector field b) Find a vector which points in the direction of the axis of rotation of the fluid at the point (2,-3,1), if the fluid rotates at the point. Explain c) Determine whether the point (2, -3 1,) is a sink or a source (ie., whether fluid is flowing into the point or out of the point,...
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)
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)
ems (1 point) A) Consider the vector field F(x, y, z) = (6yz, -7zz, zy). Find the divergence and curl of F. div(F) = V.F= curl(F) = V F =( ). 5 (5x?, 2(x + y), -7(x + y + x)) 7 B) Consider the vector field F(x, y, z) Find the divergence and curl of F. div(F) = V.P= curl(F) = V XF =( 8 9 10 )
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 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)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...
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2) is given. Find: (e) The surface integral of the normal component of the curl of F over the open hemisphere x + y2 + z = 4 above the x-y plane.
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...