29. Let K be the part of the cone z = Vx2 + y? between z = 1 and z 3, oriented upward. Let F(x, y, z) = (z, -x,1+ 2). Calculate the flux of the field through K.

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then

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Q: d) Use the curl test to determine if the following vector fields are conservative on R². If the test…

A: As per our guideline we can solve only first three subparts question. Let a vector field    F=…

Q: 10. Given F(x, y) = (x, y), find the flux of the vector field across the piece of the circle x² + y²…

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Q: 8. Let S be the filled-in square in the rz-plane with vertices (0,0,0), (1,0,0), (1,0, 1) and (0,0,…

A: Given vector field: F=-y,z,x Let A(0,0,0), B(1,0,0,), C(1,0,1) and D(0,0,1) be the vertices of the…

Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid.…

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Q: A Particle moves 2 X half way around the circle y² = 4 oriented in the counter-clockwise direction…

A: Given force field: and the path of the particle moving half way around the circle  in the…

Q: Let f(x, y, z) = 3xyz + y?z. Find the gradient field Vf.

A: Formulae of gradient field is given below

Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (1, 1) along the segments…

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Q: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

A: Given vector field, So,

Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

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Q: Compute the curl of F = (3y2, ay, 22).

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Q: Find the linearization L(x, y, z) of the f(x, y, z) = 6(x3 + y3 + z3)1/2 at the point (1, 2, 3).

A: f(x, y, z) = 6(x3 + y3 + z3)1/2We have to find linearization L(x,y,z) of f(x,y,z) at point (1,2,3)