Find the line integral of the field F =< 3x²yz + 2y²z?, x°z+4xyz², x³y+ 4xy²z > over the straight-line path from (1,1,1,) to (2,2,2).

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: 4. Is this vector field F(x,y)=(ycos x)ĩ +(sin x+ y)j being the path-independent field? Please show.

A: To check if the given vector field is path-independent field or not. Given:

Q: 10. For a vector field F = 2xy+ y³, x² + 3xv²+ 2yZ find a function f such that F = VI. www

A: We have to find the function

Q: Find the wark done by the Foree Field FoK x>ye^> along the parabola X=y+1 from (bo) to (2,1).

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Q: Suppose the slope field given below is for the equation u' = f(t, u). Draw a possible solution for…

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Q: Given the vector field A = (x²+y²) ³/4 (x +yy), → 1) Calculate the line integral of A from the…

A: Q-1The vector fieldA→=1(x2+y2)3/4(xx^+yy^)The line integral from the point origin to (0,1,0)(I) Let…

Q: Given the vector function *(t) = (t, cos (2t)) Calculate the curvature when t=5.4

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Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

A: If we are given a plane equation in the form Ax+By+Cz=D, then the normal vector to the plane will…

Q: F(1, y, 2) = (2c" cos(3y), –3e²" sin(3y) + VV:). a. Find divF(x, Y, 2) and curlF(x, y, z). b. Based…

A: This is a problem of multi-variable calculus.

Q: 8xz Calculate line integral F. dr of conservative vector field F(x, y, z) = i Y A from (-4, 2, 1) to…

A: we have to find the line integral  ∫AF.dr where F(x,y,z)=8xzyi-4x2zy2j+4x2yk and A is path from…

Q: A conservative vector field is given as F = 6xe'i + (3x²e' –10yz')j-15y 2 k. Find the potential…

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Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

A: Given F→=y,x+2y We have to find the ∫CF→⋅dr along the given path.

Q: Find the Curl of the vector field. F(x,y, 2) = 1le sin y i+ 12e* cos(y j+3z k a. (12e* cos(y) +1le"…

A: Curl of a vector can be calculated by forming a matrix and then finding the determinant of the…

Q: For Vector fields with va (X.X)= x VY (X. y) = y X U* (x.y) =~Y U (x.x) = x Compute the Lie…

A: Given: Vector Feilds with Vxx.y=x   Vyx.y=yUxx.y=-y  Uyx.y=x We need to compute the Line derivative…

Q: Determine the signs of the line integrals for the pictured vector fields and curves. C₂ (a) (b) C₁…

A: The sign of line integral decided with the help of angle formed by curved and vector filed. Since…

Q: Sketch the slope field for the points (ti, y;) where at and dy dt y-2 Z₁ = -1 + 0.25(1-1) = for…

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Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

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: Sketch the slope field for dy/dt = y sin t for −2π ≤ t ≤ 2π, −2 ≤ y ≤ 2.

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Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

A: Given field is,  F = yz i^ + xz+3 j^ + xy k^   The given points is A(1, 2, 0) and B(2, 0, 3). So,…

Q: F - () (3x²y²z and F = 2r³yz Q.)11.1 Be (a) Explain why vector fields are conservative. (b)…

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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: Apply fundamental theorem for conservative vector field to find the line integral fF dr where F =…

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Q: 1) For the vector field F(x, y) =−x²'yi + xy²j, find the following: a) Find the 2D curl of this…

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Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: 13. Let V = xi+yj (a) Give reasons why V(x, y) is a vector field (b) Sketch the vector field V(x, y)

A: (a) Consider the given Vector, V=xi+yj The definition of vector field is given as " A vector field…

Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

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Q: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

A:

Q: Show that the vector field 1 F(x, y, z) = (- :)= (-2: 25³ sinh (2y − 1) - x²y is conservative by…

A: If a vector field F→(x, y, z) is conservative then there exists a potential function f(x, y, z) such…

Q: Find the divergence of the field. F = 3ye5xyzi + 3ze5xyzj +3ye5xyzk

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Q: Therefore, div(curl G) = sin(y) – sin(y) + 8 = Since div(curl G) is different from 0, we conclude…

A: Given that:div(curl G)=siny-siny+8=