1. Consider the vector field F%3= (7.ryz, 5a z, 2²yz) . Identify the potential function for the vector field F. (a) The potential function of F is f(z, y, z) = x²y²?. (b) The potential function of F is f(2, y, z) = 2r²y"z°. (c) The potential function of F is f(z, y, z) = x²yz + 5ry?z²?. (d) No potential function exists.

Q: How do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?

A: Given: vector field

Q: ey+y°.

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Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: Let f(x,y) = sin x+sin y. (NOTE: You may use software for any part of this problem.) %3D (a) Plot a…

A: (A) plot the contour of f.

Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: y² cos(xy?) – ay sin(æ²y) Let it be 7 : R² → R², (2ary cos (ay?) – ža² sin(a²y)/ a vector field.…

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Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

A: The given vector field is  F⇀(x,y)=2xy3i⇀+3y2x2j→ We have to show that F→ is conservative

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Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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Q: Determine if the vector fields below are conservative. Find potential functions where possible. (a.)…

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Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: (a) Calculate the flux of the vector field F(x, y, z) = 27 - 4k through a sphere of radius 3…

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Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

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

A: we have to find potential function.

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Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: Compute the curl of the vector field F = -4zi - 5y 3-4x k. =url= =

A: Given,  The Vector Field,F→=-4zi-5yj-4xk The Curl of the vector field is to be calculated.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…