Calculate the work done in moving a particle in the vector field: F = xz i+ xy²j + 3xzk along the intersection of the plane x + z = M and the cylinder x² + y2 = M + 2, inthe counterclockwise direction. M- The last digit of your matrix number For example, a student with the matrix number CD200079 will have the values of M = 9. Use 1 if the last digit is of your matrix number is 0.

Q: Compute the circulation of the vector field F = in moving a particle around the path showed in the…

A: From Green's theorem of circulation form Work done on a particle by force field F→=Px,y,Qx,y is…

Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

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Q: Assume that Ax, y, z) is a vector field whose i component is only in terms of y and z, whose j…

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Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: Verify that the work performed along the segment P Q by the constant ~ vector field F = (2, -1, 4)…

A: We have given; vector field F = (2, -1, 4) (a) P = (0, 0, 0), Q = (4 , 3, 5) (b) P = (3, 2, 3), Q =…

Q: Solve numerically for The scalar projection of vector u onto v

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Q: Compute the outward flux of the vector field

A: Given,         F(x, y, z)=x3i+y3j+z3k And S is the surface of the solid bounded by the cone…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi – 2xzj + yzk; (9, -9, 5)

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Q: Match the vector field with its graph. F(x, y) = yi 5 5 -5+ サ

A: To match the given vector field to its graph, where given graphs are given below.

Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

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Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: 22 Calculate the work done in moving a particle in the vector field: F = xz i+ xy2j + 3xzk (a) along…

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Q: Sketch the vector field in the plane along with its horizonta and Vertical a representative…

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Q: If F1 and F2 are two forces simultaneously acting on anobject, the vector sum F1 + F2 is called…

A: We know, The vector sum of all of the forces acting on a body is a single force called the net force…

Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b)…

A: To Determine : (a) F(x, y) = (xy,y − x)(b) F(x, y) = (4, 8)(c) F(x, y) = 3x+y , log2(x + y) Given:…

Q: 4b. Find a "vector potential" for V, i.e. a vector field W such that curl(W): method - don't just…

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Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: What does it mean to say that a vector field is conservative?

A: What does it mean to say that a vector field is conservative?

Q: Find the curl of the vector field at the given point. F (x, y, z) = x²zi - 2xzj + yzk, (2,–1,3)…

A: The solution as follows :-

Q: What are the outputs of a vector field in ℝ3?

A: What are the outputs of a vector field in ℝ3.

Q: Match the vector field with its graph. F(x, y) = yi -5+ -5+

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Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 9)

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Q: Let x and y are orthonormal vectors in R". Then ||x - yl| is a) o b) c) d)

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: b) Plot the vector fields for different values of h (show all qualitative behaviors)

A: The given equation is, dxdτ=x1-x-h So, the vector field for different values of h are as follows.

Q: Find the gradient vector field of flx, y, z)=x'y+y%z4+xz6 O V flx, y,z)= (3x?y+z°, 5x³y³ + 4y*zA,…

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Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

Q: of the vector field Parye" + around the boun 4. and y = 4.

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Q: Construct tne vector -a-bhaving initial point P.

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (9, -9, 7)

A: The curl of a vector field F is defined as  ∇×F=i^j^k^∂∂x∂∂y∂∂zf1f2f3

Q: Let S be the flat, shaded surface oriented as shown by the normal vector n in the diagram above.…

A: consider the equation

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: Is the vector field shown in the figure conservative? Explain

A: The conservative vector fields are the path independent vector fields. A vector field, is…

Q: Use Laplace transform to find a fundamental set of vectors for the system of ODES %3D

A: Step:-1 Note:- Lf'(t)=s F(s)-F(0) Given that x→'=1221x→ Let  x→(t)=x(t)y(t), Here we take t as…

Q: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: Find the gradieat of the functionf = xyz-4y2z. Visualize the vector field of the gradient. %3D

A: In vector calculus, the gradient of scalar valued function denotes the direction in which the…

Q: Find the stable vector of

A: Given information: In the given Markov model, there are 2 states. A state transition matrix consists…

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi − 2xzj + yzk; (9, −9, 1)…

A: Given function is F(x, y, z) = x^2zi − 2xzj + yzk; We find curl F at (9, −9, 1)

Q: Select the option that gives the vector field that could correspond to this arrow map.

A: The vector field is when a vector is assigned to each point in the given space. The cartesian form…

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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Q: Compute the flux of the vector fieldi = -3 i+ 4j- 2 k through the rectangular region shown below,…

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