Let S be the portion of the cylinder y² + z² = 4 with z > 0 between the planes r = 0 and a = 5 oriented upward. Let %3D F(r, y, 2) = (x², y², z²), compute the flux of F across S.

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: 4. Find the flux of F across S if F = yi-xj+2zk and S is the hemisphere x² + y² + z² = 4, z ≥ 0,…

A: We have to find flux passing through sphere.

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 the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: Sketch the level curves f(r,y) = c of the function f(x,y) = ln(r² + y²) for c = -1,c = 0,c = 1,c =…

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Q: 2 x = 8 - y, x =y - 8

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Q: :::.. V : 5+j wi +4j Find the specific Scalar .(.. )

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Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

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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: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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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 gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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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: Let f(x, y) = 4x² + 5y³ A) Find the equation of the plane that passes through the point (2, -2, ƒ(2,…

A: Given f(x,y)=4x2+5y3 Now f(2,-2)=16-40=24 fx=8x,fy=10y2 Solution a: Equation of plane passes through…

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: Find the centroid

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Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: The separation vector can be written as R = (x – x')ê+ (y – y')ŷ + (z - z')2, Find

A: Given,             R→=(x-x')x^+(y-y')y^+(z-z')z^

Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: Let F = –9zi+ (xe"² – 2xe³) }+ 12 . Find ſg F ·dÃ, and let S be the portion of the plane 2x + 3z = 6…

A: The vector field is F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plane is 2x+3z=6⇒ gx, y=6-2x3.…

Q: Find the flux of F = yi+2xj-3zk through the unit disk centered at (0,3,0) in the plane y=3, oriented…

A: Given F→=yi^+2xj^-3zk^ through the unit disk centered at 0,3,0 in the plane y=3 oriented towards the…

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: Find the flux of F= (y, z-y, z). across the tetrahedron with vertices (0,0,0), (1,0,0), (0, 1,0),…

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

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