Compute the line integrals of the vector fields F. Graph the region of integration C F(x, y, z) = xî + yzĵ – (xy – zx)k, along the line segment with endpoints (0,0,0) and (1,2,2)

Q: 6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify…

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Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

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…

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Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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Q: 3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along…

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Q: se the given transformation to evaluate the integral. J 6z + 3ydA, where Ris the parallelogram with…

A: we have given: x=13u+v and y=132u-v  u=x+y, v=2x-y Now, Consider the integrals, ∬R6x+3ydA where, R…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z)=tan(4x+y+z). F(x, y, z) -

A: Solution:-                The given function is f(x,y,z) = tan(4x + y + z) then we have to find…

Q: 5. Solve the following problems: (a) Choose, refer and use one of the theorems of Vector Calculus to…

A: Solution: Given, F→  = M,N = <-xy-5, -2x-3y2> To calculate,

Q: Find the gradient vector field (F(x, y, z)) of ƒ(x, y, z) = x³y³ z z F(x, y, z) =

A: Solution :-      The given function is     f(x,y,z) =  x6y3z4   then , we have to find gradient…

Q: f(x. y.z) = + xy + yz + Q8) Find the Linearization at (1,1.2)

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Q: where r is the position vector 6. Show that A) - da = | (Ax (Vf)) · da + fA- dl 7. Evaluate the…

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Q: (2x+yy), (x²+y²)3/4 → 1) Calculate the line integral of A from the origin of the coordinate system…

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

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Q: Let F(x, y, z) = (x², 2xy + e³², 3ye³z). Find div F(1,2,0) and curl F(0, 1, 1).

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Q: Find a function f(x, y, z) such that Vf is the constant vector (7,5, 4). (Use symbolic notation and…

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Q: 1. Find a vector valued function that represents the curve of intersection of the semi-ellipsoid x²…

A: The equation of the semi-ellipsoid is The cylinder is

Q: 4. Match the vector fields given below with their plots. (a) F(x,y, z) = (b) F(x, y, z) = (c) F(x,…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(2x + 3y +6z). F(x, y, z) = 2 Check…

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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)

Q: If F = xy i+ (x² + 4yz)j+ 2y²z k. Evaluate the line integral between A (0, 2, 0) and B (3, 6, 1).…

A: Given, F= xy i +(x²+4yz)j +2y²zk r0= (0,2,0) r1= (3,6,1)

Q: Suppose the vector field v(x, y, z) = (3z+2) i+(4x+1) j+(3z+1) k represents the velocity field of a…

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Q: t F (x, y, z) = (x + y²z, y³ + z³). Calculate the linearization of F at (1, 2,3).

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Q: Calculate line integral A from (3,-7, 7) to (0,5,-3). F F. dr of conservative vector field F(x, y,…

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Q: Find a vector normal to the cylinder x2 + z2 = 8 at (2, 0, 2) by finding the gradient of the…

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