Let R' have the Euclidean inner product and let u = (1,-2,-1) and v = (3, 1,0) Then proj, u %3D

Q: Let Li be the straight line segment from (0.0,1) to (1,a, 8) and let F: (z+ax, ay, x> Calculate the…

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Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: An inner product on R² is defined as (u, v) = (Au) · (Av), [ 3 where A : -3 (a) Is (1, –2)…

A: Orthogonal Vectors: Two vectors x and y in an inner product space are called orthogonal, if x, y=0…

Q: Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices…

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

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Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: Let u = (x²yz, ry z, ryz?). Compute curl i

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Q: find laplace of f(x,y,z)=2x3y2z2

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Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: please explain this solution (orthogonal projection onto W) 1 1 1 1 1 1 1 0 0 1

A: Given: To explain the given solution as follows,

Q: Use Green's Theorem to evaluatc the integral x²ydx + xydy where C is the rectangle with vertices (0,…

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Q: Show that the vector field F = 2xyi + (x² – 2 y)j is conservative and evaluate the line integral…

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Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x F(x, y) = -

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Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

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Q: Show that the vector field F=2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

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Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: Find work done by a force field F= in moving object along the line segment from the point (2,1,3) to…

A: Given, F=1y-x,xyz,ex2+y2+z2

Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Show that F of F. = (2xy + z³)i+x²+3xz²k is conservative force field. Find the scalar potential

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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

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Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: Evaluate the double integral || 8xydA, where Dis the triangular region with vertices (0,0), (1,2),…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

A: Given that F→x,y,z=4,x9-y2,6z

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: Let i = (x²yz, ry z, zyz?). Compute curl i

A: The given vector is: u→=x2yz, xy2z, xyz2

Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence

A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…

Q: Evaluate the double integral. 6y? dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

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Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

A: Given that,

Q: 2. Verify that the usual length of Vector in the has the plane properties in 3 dinensional Space…

A: Given: usual length of a vector in the plane or in 3 dimensional. To prove that this vector has the…