Question

Curl and Divergence: Problem 7 (1 point) For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F??= 3yzi + (3xz + z^2) j + (3xy + 2yz) k: curl F = < 3yz,3x^2 + z^2,3xy + 2yz > F is a gradient field (b) G = 3yzi + (z^2 - 3xz) j + (3xy + 2yz) k: curl G = G ? (c) H = (6xy + x^3) i + (3x^2 + z^2) j + (2yz - z) k: curl H = H ?

          Curl and Divergence: Problem 7
(1 point) For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) F??= 3yzi + (3xz + z^2) j + (3xy + 2yz) k:
curl F = < 3yz,3x^2 + z^2,3xy + 2yz >
F is a gradient field
(b) G = 3yzi + (z^2 - 3xz) j + (3xy + 2yz) k:
curl G =
G ?
(c) H = (6xy + x^3) i + (3x^2 + z^2) j + (2yz - z) k:
curl H =
H ?

Curl and Divergence: Problem 7
(1 point) For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) F??= 3yzi + (3xz + z^2) j + (3xy + 2yz) k:
curl F = < 3yz,3x^2 + z^2,3xy + 2yz >
F is a gradient field
(b) G = 3yzi + (z^2 - 3xz) j + (3xy + 2yz) k:
curl G =
G ?
(c) H = (6xy + x^3) i + (3x^2 + z^2) j + (2yz - z) k:
curl H =
H ?

Added by Carlos D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hemraj Kumawat

07/28/2022

Step 1

(a) F = 3y^2z i + (3xz + 2)j + (xy + 2yz)k The curl of a vector field F = P i + Q j + R k is given by: curl F = (∂R/∂y - ∂Q/∂z)i - (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k So, curl F = (∂(xy + 2yz)/∂y - ∂(3xz + 2)/∂z)i - (∂(3y^2z)/∂z - ∂(xy + 2yz)/∂x)j + (∂(3xz + Show more…

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Curl and Divergence: Problem 7 For each of the following vector fields, find its curl and determine if it is a gradient field: (a) F = 3y^2z + (3xz + 2)j + (xy + 2yz)k curl F = 3yz, 3x^2 + 2, -2xy + 2z Not a gradient field (b) F = 3y^2z + (2 - 3xz)j + (3xy - 2y^2)k curl F = 3yz, -3x^2, 3x - 4y Not a gradient field (c) F = (6xy + x')i + (3x^2 + 2)j + (2yz - 2)k curl F = 0, 0, 0 Is a gradient field