Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing normal: F = (e² 2,0,0), the square with vertices (2,0, 7), (2,2, 7), (0, 2, 7), and (0, 0, 7). ScF-ds . = ff curl(F). ds =

Q: you represent this relationship mathematically? gent vector v at (xo Yos Zo)? How 2. Consider a…

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Q: Find r'(t), r(t), and r'(to) for the given value of to r(t) = (1+t)i + ³j, to = 1 (No Response)…

A: We have to find the values of r't, rt0, r't0 where rt=1+ti^+t3j^, t0=1 and sketch the curve…

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: Use Stokes' Theorem to find the circulation of F = 4yi + 4zj+ 3xk around the triangle obtained by…

A: We have to find ∫CF→·dr→ using Stokes'sTheorem

Q: Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) =…

A: rt=et,e2t,t0=0

Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (1,-4)…

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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: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

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: 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: Compute the normal vector to the surface Ф(и,0) %— (и? — 0?, и +0, и — 0) at that point (4,3).

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: What is the normal vector of the corresponding scalar equation of the following plane? r` = (2,−5,2)…

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: Find the unit tangent vector T, the unit normal vector N, and the binormal vector B for curve r at…

A: Here we are given the curve r(t)=(7cost,7sint,7ln(cost))We have to find the unit tangent vector…

Q: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

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Q: A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the…

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Q: Write formulas for the unit normal and binormal vectors of a smooth space curve r(t)

A: The formulas for unit normal vector  and binomial vectors of a smooth space curve r(t).

Q: Use Stokes' Theorem to find the circulation of F= 2yi +423 +3ack around the triangle obtained by…

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Q: Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).

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Q: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: t) = (et, e24), to = 0 لاخت لا rve represented by the vector-valued function, and sketch the vectors…

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Q: Sketch the curve with the given vector equation by finding the following points. r(t) = (2, t, 4-t²)…

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