Find the curl of the vector field F = (3y cos(x), 5x sin(y))

Q: Find the curl of the vector field F (5x sin(y), 2y cos(æ)) curl F =

A:

Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

A:

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

Q: Find the work done by the vector field f = to move a particle along the arc of the hyperbola y=1/x…

A:

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

A:

Q: Compute the curl of the vector field F = - (x + 3y) i + (y – 3z) } – (z + 3x) k curl

A:

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y) =…

A: It is required to find the conservative vector field for the potential function given in the…

Q: 13 Is this vector field F(x, y)=(ycosx)i +(sin x+ y)j being conservative? Please show.

A:

Q: Find the curl of the vector field F = (3y cos(x), 6x sin(y)) curl F = %3D

A:

Q: Integrate the vector field over the curve C. F (x,y) =(y+1, 2x) C: x=4t, y=t², 0<t<1

A:

Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

A:

Q: Find the gradient vector field of f(x,y) = x2 + y2 and sketch it.

A: Solution

Q: Find the gradient vector field of f(x, y) ,3

A: Given,          The gradient vector field of fx,y=x6y3.

Q: Determine if the vector field F=(yz,xz,xy) is conservative?

A:

Q: Evaluate line integral of vector field F(z,9) = i+ 1- x? y2 2x along the curve x = cos(t), y =…

A:

Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

A:

Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, у, 2)…

A:

Q: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Find the gradient vector field of f(x, y) = tan(2x − 3y).

A: Given fx,y =tan2x-3y         we find the gradient vector of fx,y

Q: Find the curl of the vector field F curl F = (2y cos(x), 5x sin(y))

A: F = (2ycosx , 5xsiny) find curl F =?   curl F  = dF2/dx - dF1/dy here  F1 = 2ycosx  F2 = 5xsiny now…

Q: Determine if the vector field F is conservative. F= cos x cos yi + sin x sin yj - sec |- sec zk O…

A:

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y) = x²…

A:

Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

A:

Q: Find the gradient field associated with the function φ(x, y, z) = xyz.

A: To find the gradient field associated with the function  φ(x, y, z) = xyz.

Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

A:

Q: Find the curl of the vector field F = (4x sin(y), 7y cos(x)). curl F - Dretieur

A:

Q: Find the curl of the vector field F = (7y cos(x), 5x sin(y)) curl F II

A:

Q: Find the curl of the vector field F = (6y cos(x), 7x sin(y)) curl F =

A: If  F=f1x,y, f2x,y   thenCurl F=0,0,∂f2∂x-∂f1∂y

Q: Find the curl of the vector field F. F(x, Y, 2) = arcsin yi+ V1 - xzj + yêu y²k

A:

Q: Find the gradient vector field of f(x, y) = ln(4x + 2y)

A:

Q: Find the curl of the vector field F = (3x sin(y), 7y cos(x)).

A: The solution is:

Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

A:

Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

Q: The movement of air on the surface of a certain closed controlled space is studied, and every point…

A:

Q: F=cos(x) î+sin(y) ĵ+cos (z) k

A:

Q: Express the field D = (x2 + y)-(xax + yay) in cylindrical components

A:

Q: Find the flux out of the curve bounded by the top half of = arccos(√√²+² ) and y=0 with vector field…

A: As per the question we are given a bounded curve C and a 2d vector field F And we have to find the…

Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field

Q: Find the curl of the vector field F = (3y cos(x), 4x sin(y)). curl F = %3D

A:

Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

A:

Q: Find the counterclockwise circulation and outward flux of the field F = 7xyi + -5y²j C enclosed by…

A: Introduction: Let C be a piecewise smooth, simple closed curve enclosing a region R in the plane.…

Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

Q: find the curl for vector field F = y³i+ xyj – zk

A:

Q: The integral of the vector field F(x, y) = (cos |x|, sin y|) A = (-2,0) and final point B (0, 2),…

A: Correct answer is (B) sin(2) - cos(2) + 1 Explanation:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

A: