- Given the vector fields Å = yz az – 3x a, +x²y a, B = 3 a, – 4xy a, +y² az Petermine a unit vector perpendicular to both Ả and B at (1,2, 3).

Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,y) Choose the correct answer below. O…

A: Make a table by considering some points and form from and to points as shown in step 2. Then plot…

Q: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

Q: If the vector field v = [mz+x, -y, x]is irrotational, the mis equal to O A. 2 O B. 0 O C. 1 O D.…

A: Curl of v is zero.

Q: Given vector field A = 5p sinø a, - pz cosø a, + 2p a̟. At point P(1, T, -1), the vector component…

A: A= 5ρsinϕaρ-ρzcosϕaϕ+2ρaz  at point  P(1,π,-1) =0aρ-1aϕ+2az A that is parallel to  ϕ =π is…

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: a Compute the flux of the vector field i = -2 i + 5j – 4 k through the rectangular region shown…

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Q: of the following vector fields, the one that is conservative corresponds to: 3xy¹+x A) F(x, y, z) =…

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Q: 4. Consider the vector field given in Cartesian coordinates by A(r) = (x² + y³, 3xy², z²). (a)…

A: Given : Ar=x2+y2,3xy2,z2

Q: Which of the following vector fields matches the plot below? -2 -1 1 -D1 -2 1 F(2, y) = i - 7 %3D 1…

A: Given the vector filed,  To match the vector field with the given plot.

Q: Find the work done by the force field F(r, y) = (2ry², 2x²y + 1) in moving a particle along any path…

A: The given force field is:  F(x,y)=2xy2, 2x2y+1

Q: Find the flux out of the unit shpere for the vector field F(2,4, ;) = 1ā+3+K). %3D r answer =

A: Flux of F through the closed surface S is ∫∫sF→·n→dsS is the unit sphere x2+y2+z2=1Letϕ:…

Q: What is the value of a so that the vector field F(x.y)=(In y+2xy³) i+(ax²y2+ x/y) j is conservative?…

A: To find: the value of a for which given vector field is conservative.

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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Q: b) Given the vector field SUTM F(r, y, 2) = 3z cos ri+rlnyj+e* tan rk. Determine UTM i. div F, ii.…

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Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

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Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

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Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax?y3+ e%)j is conservative? O…

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Q: Compute the flux of the vector field v = -4 i+ 3j+5 k through the rectangular region shown below,…

A: Given  v→=-4i→+3j→+5k→ a=1 and b=3

Q: If a vector field A(x,y,z)=xz°ex - 2x yzey+2yzez , calculate the curl 7xA at point M(1,-1,-1).

A: A vector-valued function is a rule used to fix a vector to a particular point in space. The general…

Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

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Q: Determine the vector field of F. F(r, y) = 4i – 2j

A: To determine the vector field F .

Q: A vector field is given as G = (1/(√x² + xy))(e¯²ax +xzay), find the unit vector which is normal to…

A: The given vector fields are: G=1x2+xye-zax+xzayP=3x2ax-4yay We have to find the unit vector which is…

Q: Which of the following vector field is not conservative? a) Å(r, y) = yi- 3ryj b) 72r + 14(x² +…

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Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

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Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: At how many points is the vector field F(x, y, z) = (z– ,r – 2², y – x²) irrotational? Select one:…

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Q: Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four…

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Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: A constant field vector is given by E = -5a_p + 10a_0 + 3a_z. Calculate the vector component of E at…

A: The problem is related to vector. The topic is multidimensional geometry. We find the component of…

Q: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Compute the curl of the following vector field. = (6xz° sr. 5xz e 6 ey 6xz° eY) 6. The curl of F is…

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Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

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Q: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

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Q: If r(t) = (1 + t)/²i+ (1- t)/2j+tk, t 0 then the binormal vector B is اخترأحد الخيارات

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Q: 2 determine the vector evaluated at (2, n/2, n/4). Given the vector field E=rcoso a,+ sine ae +ra

A: Given vector field is The point is From the point:

Q: (20) Given the vector field i = (a² – y² + 2xz)î+ (xz – ry + yz)ĵ+(2² + x²)k. Find v x ở and show…

A: Given v→=x2-y2+2xzi^+xz-xy+yzj^+z2+x2k^

Q: o) Find the flux of the vector field F (x,y,z) = 3xi – yj + 2zk; across o where o is

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: What is the value of a so that the vector field F(x.y)-(y eX+2xy4) i+(ax²y3+ e%)j is conservative? O…

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Q: What is the value of a so that the vector field F(xy)=(In y+2xy³) i+(ax3y2+ x/y) j is conservative?…

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Q: Compute the flux of the vector field F⃗ =xi⃗ +3yj⃗ F→=xi→+3yj→ through the cylindrical surface shown…

A: Given that the vector field is F(x,y)=xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: A. Find the flux of a vector field = 8x i + 6y j+ 2z k through the portion of the plane z = 7 where…

A: As per the guidelines, I am supposed to do the first question only. Kindly repost the second…

Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

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Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

Q: given the vector field A(ρ,φ,z)= cos(φ)*ρ+ e^-6z *φ+ 6*z find the laplacian and evaluate it at the…

A: We have to find the Laplacian at the guven point.

Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: The work done by a force (3i + 4j + 5k) N acting on a particle which moves from a point with…

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Q: Q9. V = 2yī – xJ, what is the magnitude and direction of the vector field made with the 5, 26.6° V5,…

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