Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the direction vector (2,-1,-2):

Q: Find the directional derivative of the scalar field = x¹y + 4xz at the point (2, -2, 4) along the…

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Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-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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Q: Find the equation of the gradient vector field for the function f(x, y) = – læ² + 1y and then sketch…

A: The gradient vector field of given function is -2x i + 2y j

Q: Find the gradient of the function f = xyz-4y z.

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Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

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Q: he surface al derivative

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Q: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

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

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Q: he position of a particle is determined by the vector-valued function r(t)=. Find the decomposition…

A: Given position of the particle We have to find the decomposition of the acceleration vector in terms…

Q: f f(x, y, z) = xy: on of vectorî - %3D

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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: F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?

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Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

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

A: we have to find potential function.

Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: A constant field vector is given by E = -5a_p + 10a_0 + 3a_z. Calculate the vector component of E at…

A: The problem is related to vector. The topic is multidimensional geometry. We find the component of…

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,Now,calculate the…

Q: nd the increase rate of the scalar V at point P from origin to the point P(12 , 1,11 here V=…

A: As gradient of a scalar function gives the magnitude and direction of rate of change.

Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: Describe a non-zero vector function r(t) in R^3 whose acceleration vector a(t) satisfies a(t) =…

A: Solution is given below:

Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

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Q: Find a potential function for the vector field .F(x,y)=

A: The vector field is

Q: What is the curl of a vector field? How can you interpret it?

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Q: Calculate the work done by the force field on the particle.

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