Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation r(u, v) = (u cos v, u sin v, v), 0 ≤ u ≤ 1,0 ≤ y ≤ 8.

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

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Q: Let the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=3x…

A: Here I am attaching image so that you understand each and every step.

Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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Q: Let the temperature / in degrees at the point X,y,z), with distances measured in cm, be T(X,y,z)=5x…

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Q: 1- a) c) −2ñi + (2ñ + 1)j b) 2πi + (2π − 1)j - 4пi – (2n + 1)j 2лi + (2π + 1)j 4ñi + (2ñ + 1)j Leave…

A: Given:The given function is .To Find:We have to determine the gradient vector of  at the point…

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: 2yz - 2yz2 + x at the point p = (1, -1, 1), find the unit vector that indicates the direction in…

A: Introduction:   The gradient of the temperature function at the point is the direction of the…