Which of the (i) F(x, y) = (10xy+6) i + (9xy+8) j (ii) F(x, y) = (9ye⁹x + cos 6y)i + (x + 6x sin 6y) j e10xy j (iii) F(x, y) = 10y²e1¹0xyi + (10+xy) e¹ following vector fields are conservative?

Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 3) to (9, 3), and the line segment…

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Q: 20) For each vector field F, evaluate the circulation along the curve C consisting of the portion of…

A: Step 1:Step 2:Step 3:Step 4:

Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

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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: Suppose f(x, y) = sin( (a) Vf(x, y) = = (b) Vƒ(3, π) = 2y x T 2y 2y 2y cos cos 2) Con (2) 200m (20 -…

A: Given that , fx,y=sin2yx and u is the unit vector in the direction of 1,1.

Q: For each of the following, compute the line integral S. F dr Where Cis a curve with…

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Q: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

Q: Find the Curl of the vector field. F(x,y, z) = 7e" sin(yi+ 8e* cos(y j+ 14z k a. &e" cos(y) +7e"…

A: solution of the given problem is below...

Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

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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: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Determine if the vector fields below are conservative. Find potential functions where possible. (a.)…

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Q: Prove that (Y - Y1)'(Y - Y1)= (-Y1)'(- Y1) + (Y-P)'(Y-P) where Y = n 1 Y and 1 is an n-dimensional…

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Q: 4. Match the vector fields given below with their plots. (a) F(x,y, z) = (b) F(x, y, z) = (c) F(x,…

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Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² − 2yz)j + (2x= − y²) k. (a) Show that h is a…

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Q: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve that consists of two line…

A: Given that  Fx,y = xy2+2x+1 , x2y - 3y is a vector field. Let C be the curve that consists of two…

Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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

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Q: Sketch the given vector fields by drawing some representative vectors. (a) F(x, y) = (x − y) î+xî…

A: Given:  a F→x, y=x-yi^ +xj^b F→x, y=y, -xx2+y2c F→x, y=2yj To sketch the given vector field.