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the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); +...
b- Consider the vector field F(x,y,z)= (3x²y2-3ze, 2xy +2sin z, - 3x02 + 2ycos z). (a) if f(x,y,z) = axºy2+be*2 + cysin z then a =......, (b) Use the fundamental theorem of LINE INTEGRAL to evaluate Y = SF-di along the curve defined by the parametrization F(t)= (1, sint, t-T) for Osts. Y = ...... b Choose... Y = Choose.... Choose... Choose...
Consider the vector field F (x, y, z) = <y?, z2, x?>. Compute the curl (F). Use Stokes' Theorem to evaluate S. F. dr where C is the triangle (0,0,0), (1,0,0), and (0, 1, 1) oriented counter-clockwise when viewed from above.
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
Use Stokes' theorem to find the work done by the force field F(z, y, z)-<-r, z, y > along the positively oriented curve of intersection of the cylinder 2+y 1 and the plane 3x +z 4 9. Use Stokes' theorem to find the work done by the force field F(z, y, z)- along the positively oriented curve of intersection of the cylinder 2+y 1 and the plane 3x +z 4 9.
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
Use Stokes Theorem to evaluate ØFodi for a vector field, с 3 7=(3+ E = (x+4z, -xy, y² where is the intersection of the cylinder 3 x2 + y2 = 4 and plane y + z = 3 oriented counter clockwise as shown in Figure 1. y+z=3 Figure 1
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis. Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,