Use Stokes' theorem to evaluate / (curl F· N) dS for the vector field and surface. F(x, y, z) = 6yi + zj + 4yk and S is the hemisphere z = V9 – x² – y² using the upward normal vector

Q: 2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

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Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

A: The equation is x2+y2=25 and the point is P4, 3, 6. Now, the unit normal vector is n^=∇ϕ∇ϕ. Now, for…

Q: a) Identify and sketch the surface with the given vector equation: r(u,v)=, u between 0 and 2pi, v…

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Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Calculate the curl(F) and then apply Stokes' Theorem to compute the flux of curl(F) through the…

A: The given problem is to find the curl of the given  field and also to find the flux of curl of the…

Q: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

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Q: State and illustrate Stokes' Theorem using the surface of the cone z= √√²+y³ and below the plan z =…

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Q: Compute the unit normal vector field that will give the surface parametrized by r(u, v) = (e"…

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Q: 2. Find a unit normal vector to the surface x + y +2 = 5 at the point (0, 1, 2). Ans. Û + 2k)

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Q: For the vector function: r(1)=(Sf,21,5). find %3D (a) r'(t) and r'(4) vileuponi od yd bolbni PA pe…

A: The derivative of a vector function is obtained by differentiating all the components of that…