– y² and consider the vector field F Consider two distinct points P1, P2 on the surface S. Find the value of the constant a so that Let S be the surface z = x (4xz + axy², yz, 5y²). So, F· dr = Sc, F dr for any two curves C1, C2 on the surface S from P to P2.

Q: ector product of two vector fields: V × (F x G) = (V · G)F – (V · F)G + (G · V)F – (F · V)G %3D

A: Part iii Given, The identity of the vector product of two vector fields is proved.

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Q: Let F=(9xy,7y,8z)=(9xy,7y,8z). The curl of F=( Is there a function f such that F=∇f=∇?  (y/n)

A: The given function .We have to find the .

Q: Surfaces z = x² + 2y², x + y = 0 X Parameter x = 5t

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Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

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Q: A vector field is specified as G = 24xyax + 12(x² + 2)ay + 18z²az. Given two points, P(1, 2, - 1)…

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Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: A smooth curve C is defined by some vector function R(t) with R (-) = (7,0,−2) and R′(t) = (2, √5…

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Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0, 0, 1). %3D Hint: After finding T', plug…

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A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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