5) Iff is a potential function for the vector field F = (8xy + yz, 4x² + xz - 2yz, xy - y²), then the value of f(-4, 2, 1) is: A) 110 B) 232 C) 120 D) 116

Q: Let F(x, y, z) = yi + xzj + 2xyk and G(x, y, z) = zi + xj + yk. Refine expression (FV)G (F₁0₁ + F202…

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Q: 4.) Verify the Expansion of the triple vector product A x (B x ) = B⋅ (A·C) - C (A. B) by direct…

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Q: Assuming that vector fields B (r") and A (r") in the zero infinity, check the correctness of the…

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Q: Sketch the vector field in the plane along with its horizontal and vertical components at a…

A: We shall use MATLAB to plot the given vector field on the circle.  MATLAB CODE F = @(x,y)…

Q: f is a potential function for the vector field F = (2x - 2yz, 3y2 - xz, -2xy) so what is the value…

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Q: If f is a potential function for the vector field F = (1+2ry+2:², -1+², 4x) then the value of f(-1,…

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Q: solve (D^3-3D^2+3D-1)y=x^2(e^x)

A: Solve the differential equation:  D3-3D2+3D-1y=x2exD-13y=x2exy=1D-13x2ex   y=1D-13x2ex  =ex1D+1-13x2…

Q: (3x2-2xy+3y2)dx = 4xydy Find the general solution by determining the type of differential equation

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Q: If f is a potential function for the vector field F = (y + 2xz, x - 3y²z², x² - 2y³z), then the…

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Q: If V and W are vector fields on R3 and f is a function on R3, show that: ∇ · (V × W) = W · (∇ × V)…

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Q: 11) If f is a potential function for the vector field F = (-2y + 2xyz, -2x + x²z, x² y + 8z), then…

A: To find- If f is a potential function for the vector field F = -2y + 2xyz, -2x + x2z, x2y + 8z, then…

Q: 4. Let ƒ,g be C² scalar fields on R³. Verify that V x (ƒVg) = Vƒ × Vg. V × (ƒVg+gVf). V· (SVg) =…

A: As give by the question There are given that the scalar field is f, g be C2 on ℝ3. And, In the above…

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: 3) V. (FF) = f (V. F ) + F •V ƒ. 4) V: (F +G) = V. F + v•Ğ. 5) V: (FxG) = Ġ- (V × F ) – F · (V × Ġ)

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Q: Q1: a) Sketch the vector field and find the fixed points of the following function i = x - V1 -…

A: Given equation is x.=x-1-sin2x and we have to find the fixed points of this equation. We will use…

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

A: we have to find potential function.

Q: Find the Wronskian of the following vector functions: u(t)= 5t-4 -t · -| V v (t) = -t+4 5t

A: Let  ϕ1(t)  and ϕ2(t)  are two vector valued function  Wronskian of these  vector functions is…

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: Consider the square C oriented counter clockwise, with vertices (0, 0), (2, 0), (0, 2), (2, 2) and 7…

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Q: a) Determine whether or not the vector field F 8yz, – 6 cos(y) – 8xz, – 8xy + 10z > - is…

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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…

Q: V(E × F) = F(V × E) – E(V × F). %3D

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Q: If f is a power function for the vector field F = (2xz, −3z, x2 −3y+12z2), then the value of f(−3,…

A: We have F=2xz, -3z, x2-3y+12z2 Now, F=∇f=∂f∂x, ∂f∂y, ∂f∂z=2xz, -3z, x2-3y+12z2 So, ∂f∂x=2xz…

Q: 1) Given the vector fields F1 = x²2 and F2 = xâ+ yŷ + z2, calculate the divergence and curl of F1…

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Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: Please answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz…

A: Given That : Vector field  A→=2x2yax-2(z-x)ay +3xyzaz Point P=(2,-3,4)  To Find : d) y coordinate of…

Q: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

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Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: F(x, y) = -¹ + (y-x)j 1 1 -11 1-1 1 T 1 71 1-1 1 I 1 1

A: The given vector field is F=-18i+y-xj. To Sketch: Vector field F.

Q: Find the gradient vector field of f(x, y, z) = √√√4x² + 5y² + 2z²

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Q: Let A = (A, A,y, A2) and B = (B,, By, B2) be two arbitrary vector fields, prove the following…

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Q: Q6) Given the following vector field: F = x?yi+ 2xy² j+ xyz k , Find V · F , V xF %3D and V· (V ×…

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