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22. Let S denote the plane 2x +y+ 3z = 6 in the...
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = xyzi+yj...
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = xyzi+yj + zk. S is the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8...
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant
plz onstruct and evaluate a surface integral that represents the work done by the vector field 8 in the first octant F(x,y,2)(x, 2z,3y), around the triangular section of the plane 2x+ traversed counte...
plz
onstruct and evaluate a surface integral that represents the work done by the vector field 8 in the first octant F(x,y,2)(x, 2z,3y), around the triangular section of the plane 2x+ traversed counterclockwise.
onstruct and evaluate a surface integral that represents the work done by the vector field 8 in the first octant F(x,y,2)(x, 2z,3y), around the triangular section of the plane 2x+ traversed counterclockwise.
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in th...
Use (part A) line integral directly then use (part B) Stokes'
Theorem
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward....
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
Use Stokes' Theorem to evaluate the line integral $cF.dr, where F(x, y, z) = xyzi +...
Use Stokes' Theorem to evaluate the line integral $cF.dr, where F(x, y, z) = xyzi + yj + zk, Sis the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
= and z= 8. Let A be the part of the cylinder x2 + y2 1...
= and z= 8. Let A be the part of the cylinder x2 + y2 1 between the planes z = 2, where n points away from the z-axis. Let C be the counterclockwise boundary of A. Let F(x, y, z) = (2xz + 2yz, –2xz, x2 + y²). Verify Stokes' Theorem: (a) Evaluate the line integral in Stokes' Theorem. (Hint: C has two separate parts.] (b) Evaluate the surface integral in Stokes' Theorem. Hint: curl (F) = (2x +...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
15.8 a. Use Stokes' Theorem to evaluate fF.dr where F(x,y,z) = (32-2y)i + (4x – 3y)j...
15.8 a. Use Stokes' Theorem to evaluate fF.dr where F(x,y,z) = (32-2y)i + (4x – 3y)j + (z +2y)k and C is the boundary of the triangle joining the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). b. Find F.dr where F = 2zi - xj + 3y2k and S is the portion of the plane 3x + 3y + 2z = 6 in the first octant and C is its boundary.
Find a plane containing the point (2,3,−1) and the line of intersection of the planes 2x+y-2z=22...
Find a plane containing the point (2,3,−1) and the line of intersection of the planes 2x+y-2z=22 and x+2y+3z=-14 The equation of the plane is
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = xyzi+yj + zk. S is the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant
Construct and evaluate a surface integral that represents the work done by the vector field F(x, y, z)-(x, 2z, 3y), around the triangular section of the plane 2x + y + z traversed counterclockwise. 8 in the first octant
plz
onstruct and evaluate a surface integral that represents the work done by the vector field 8 in the first octant F(x,y,2)(x, 2z,3y), around the triangular section of the plane 2x+ traversed counterclockwise.
onstruct and evaluate a surface integral that represents the work done by the vector field 8 in the first octant F(x,y,2)(x, 2z,3y), around the triangular section of the plane 2x+ traversed counterclockwise.
Use (part A) line integral directly then use (part B) Stokes'
Theorem
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT
10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
Use Stokes' Theorem to evaluate the line integral $cF.dr, where F(x, y, z) = xyzi + yj + zk, Sis the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
= and z= 8. Let A be the part of the cylinder x2 + y2 1 between the planes z = 2, where n points away from the z-axis. Let C be the counterclockwise boundary of A. Let F(x, y, z) = (2xz + 2yz, –2xz, x2 + y²). Verify Stokes' Theorem: (a) Evaluate the line integral in Stokes' Theorem. (Hint: C has two separate parts.] (b) Evaluate the surface integral in Stokes' Theorem. Hint: curl (F) = (2x +...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
15.8 a. Use Stokes' Theorem to evaluate fF.dr where F(x,y,z) = (32-2y)i + (4x – 3y)j + (z +2y)k and C is the boundary of the triangle joining the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). b. Find F.dr where F = 2zi - xj + 3y2k and S is the portion of the plane 3x + 3y + 2z = 6 in the first octant and C is its boundary.
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