2) Given vector Á = r?cos²Øâ, + zsinøâg, and function f = r?cosØ + z, find the followings: a) Div. Curl à =? b) Grad. DivÅ| =? (r = 1,Ø = t, z = 2) c) Does the Stokes theorem hold over the curve r = 3?

Q: Let F = Use Stokes' Theorem to evaluate · dī, where C is the curve of intersection of the parabolic…

A: To find the curl , ∇×F=i^j^k^∂∂x∂∂y∂∂zxy5z7y=i^7-5-j^0-0+k^0-x=2i^-xk^ To find the normal vector,…

Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² =…

A:

Q: Find the work done by a force F = 4i + 9j (in N) in moving an object in a straight line from point…

A: Given:           F=4i+9j

Q: Let F Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the parabolic…

A:

Q: Use Stokes' Theorem to evaluate  F · dr  where C is oriented counterclockwise as viewed from above.…

A: The given vector field and region C is as follows.

Q: Verify the validity of the Stokes's theorem for the vector A = e-bz sin ø a, + pe-bz , over the open…

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Q: Find the surface area of the helicoid (spiral ramp) with vector equation T(u, v) = (u cos v, u sin…

A: We need to find the area of the surface:r→u,v=ucos v, u sin v, v ; 0≤u≤1, 0≤v≤3π

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: Let F = < rY, 3z, 4y Use Stokes' Theorem to evaluate | F . dī, where C is the curve of intersection…

A: Here we have, F→=xy, 3z, 4y Using the stoke theorem, we have to evaluate the ∫CF→·dr→=? Where C is…

Q: Find the principal unit norma l r(t) = 6 cos ti + 6 sin tj + vector to the curve at the specified…

A: Given: r(t) = 6cost i + 6sint j To Find: Principal unit normal vector of the given position vector…

Q: Given the vector field F = (z,x, y), calculate the flux of the curl of F through the portion of the…

A: Given

Q: Consider the helix r(t)=(cos(3t),sin(3t),−1t). Compute, at t=π/6:  A.The unit tangent vector T= (…

A:

Q: Three coplanar forces are given as follows: A = 12 N at 90°, B = 15 N at 190°, and C = 10 N at -35°.…

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Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

A:

Q: Let F = 0, oriented upwards

A: Stokes theorem

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z2 = 9,…

A: Given that, F=x2eyz,xexz,z2exy Given hemisphere that S:x2+y2+z2=4,z≥0 From stoke's theorem, ∬Scurl…

Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

A:

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

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Q: Verify Stokes's theorem over a quarter circular disk with a radius, r = 4 in the 1* quadrant for any…

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Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: Let F = Use Stokes' Theorem to evaluate / F. dī, where Cis the curve of intersection of the…

A:

Q: 1. Compute ff,(V × F) - dS, where S is given by r² + y? + (z – 1)? = 2 and z > 0, and F(x, y, z) =…

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Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the…

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And,…

Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x? + y?…

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Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…

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Q: Use the Stokes' theorem to evaluate p Fdr where F = 3yi + yj+ :k and C is the circle r2 + y? = 3 at…

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Q: In cylindrical coordinates, a particle has position vector F = rê, + ze = r cos(0)i +rsin(0)j + zk.…

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Q: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the curve of intersection of the…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Is the integral o r(t)dt a number or a…

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Q: '. Use Stokes' Theorem to compute || CurlF •dS for the hemisphere x + y +z² =9, z20, intersected…

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Q: Three coplanar forces are given as follows: A = 5 N at 180°, B 13 N at 75°, and C = 9N at 105° .…

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Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d§, where S is the hemisphere a? + y? + z? 16,…

A: Given function is  F=x2eyzi+xexzj+z2exyk    (i) S is the hemisphere x2+y2+z2=16 , z≥0 oriented…

Q: Given F(x, y, z) = -yzį + xzj – xyzk be a vector function that passes through a surface S of z +x? +…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS,where Sis the part of the paraboloid z = 10 –…

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Q: Identify and sketch the following set in cylindrical coordinates. {(r,0,z): 0<rs5, 0<0<n/3, 1sz<4}

A: We have to draw shape of given cylindrical co ordinatie system.

Q: . Let F(x, y, z) = (x³, y³, z³). Use Gauss's theorem to find ffsF dS if S is the sphere x? + y? + 22…

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Q: Which of the following best describes the surface with the vector equation r(u, v) = (cos u)i + (sin…

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Q: Use Stokes theorem to evaluate: ∫∫Sc  n⋅(∇×F)dS, where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

A: Use Stokes theorem to evaluate:   ∫∫Sc n⋅(∇×F)dS,   where F = 5y i − 5x j + 3⋅x^4⋅y^7 k, n is the…

Q: Consider the helix r(t)=(cos(2t),sin(2t),−4t)r(t)=(cos⁡(2t),sin⁡(2t),−4t). Compute, at t=π6t: A.…

A: Given r(t)=cos2t , sin 2t   , -4t      ; t=π6

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above. yzi…

A: The given line integral is ∮CF→·dr→ Where, F→=yzi^+6xzj^+exyk^ C is the circle x2+y2=9 at z=8 The…

Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: 4. Use Stokes Theorem to find the circulation of the vector tield F around any smoo th, Simple…

A: Stokes theorem ∫CF.dr→=∫∫Scurl F.N→ ds Curl of the vector point function Ff1, f2 f3…

Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

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Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = xyzi + xyj + x²yzk, S consists of the top…

A: The given problem is to evaluate the surface integral using stokes theorem where S is the surface of…

Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? 1 (an…

A: Given that F(x,y,z)=xi+zj+2yk    ….(1) The equation of cylinder and plane is x2+y2=1  and z=x…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.