Question 4 Conservative Vector Fields Consider the vector field F(r, y, 2) (2ry:,3r ys, 4r?y="). (i) Show that F is a conservative vector field and find o such that F = Vộ. (ii) Use this to evaluate F dr, where C consists of the line segment from (1,0,-2) to (1, 1,0) followed by the curve given given by r(t) = (e", cos(t), t) for 0sts1.

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, –…

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Q: Consider the vector field v(x)

A: Given, the vector field        v(x)=yx2+y2i^-xx2+y2j^+6k^                               ...(1)

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: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: II. Let F and G be vector-valued F(1) = (1,0,2), F'(1) = (1,1,2), G(1) = (2,1,3), G'(1) = (-1,…

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Q: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

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: Question 3 Consider the vector field v(x) = i+ i+ 6k. y j + 6k. Vx²+y Vx²+y² a) Calculate /v• dr,…

A: Given vectors is vx=xx2+y2i+yx2+y2j+6k To evaluate ∫Cv·dr where C is the line joining (8,0,8) to…

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: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Recognize a vector field in a plane Sketch the vector field. x | y || F(x, y) = (1/2, − 4 ) 2 2 02…

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Q: True or False? Vector functions r 1 = ti + t 2 j, 0 ≤ t ≤ 1 , and r 2 =(1 — t )i+(1 — t ) 2 j, 0 ≤ t…

A: Given: Vector functions: r1=ti+t2j, 0≤t≤1r2=(1-t)i+(1-t)2j, 0≤t≤1 We are required to find: If the…

Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: (a) Let F(r, y) = | flow line of the vector field. Show that c(t) = ( cos(t) + sin(t), – sin(t) +…

A: To find-  Let Fx, y = yx2 + y2, -xx2 + y2. Show that ct = 35cost + 45sint, -35sint + 45cost is the…

Q: Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi

A: Given:       F = ( y , sin(x) )      viewing window :  (-2pi  ,  2pi)