Q4 If the vector filed F(x, y, z) jis given as F(x, y, z) = (-y e-xy)i – (x e¬*Y)j ,Take p = 9 i. Compute the value of curl F(x, y, z). ii. Find a function P(x, y, z) such that Vo = F(x, y, z). iii. Calculate the value of V. F(x, y, z)at the point (T,,0)

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

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Q: -y+25 Let F (x, y, z) := x+yz7 3+2⁹ let n be the outward unit normal vector. Evaluate Sf (curl F) ·…

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Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

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Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

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Q: (d) Find the value of that makes the following two vectors parallel to each other: a=-zi+3j 6=3i-j…

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A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt. n'=dxn, h' = d x b and…

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Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

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Q: Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k          B.…

A: Option (c) correct  For detail...go through the solution

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Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

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Q: The work done by the vector field F(x, y) = (-y², ²) along the arc of the parabola y = 2x² - 4x + 2…

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A: Note: As you have posted multiple question but I will answer first question according to the…

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