Determine and state the work done by the vector field over the given path in situation. F (x,y) = (x - 10.xy,2– 5x) moving from (0,0) to (4,4) to (6,2). a.

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, –9, 5)

A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k   ; (7 , -9 , 5)

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: 5. Find a potential function corresponding to the vector field F(r,y, 2) = (2r, 3y, 4:).

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Q: 8. Compute the flux of the vector field. F(x,y,z) = (2x -z,-2y, 1-2x) through S= {(x,y,z) € R³: z =…

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Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

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

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Q: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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Q: 13 Given the conservative vector field, F = (x +3y?)i +(6.xy +5)j , evaluate the 120) integral F.ds…

A: Here we use the way of line integral. By finding the parametric path between two points.

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

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Q: 15) Consider the vector field F (x, y, 2) = (In y, x, z) and the oriented curve C:r (t) = (t, e', 2…

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Q: 7) Consider the vector field F (x, y, z) = (xZ + cos y, XZ - x sin y, Xx). The work that the F field…

A: A) 10,57 J

Q: Integrate the vector field over the curve C. F (x,y) =(y+1, 2x) C: x=4t, y=t², 0<t<1

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Q: Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

A: To Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

Q: 5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential…

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Q: 8) The vector field Vp[x, y] = F =- has a potential function p[x, y] = a) (x² + y²)³2 b) d) Vx? +y?…

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Q: Determine and state the work done by the vector field over the given path in each situation. F…

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Q: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

Q: Compute the line integral of the vector field F = (3zy-¹, 4x, -y) over the path c(t) = (e¹, e¹, t)…

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Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

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Q: 5. Given the vector field F(x, y, 2) = (2x In y|+ 2°|2yz) find the following a. Gradient of . b.…

A: As per Bartleby guidelines, for more than three sub-parts asked for a question, only three is to be…

Q: 3. Use the fact that F = is a conservative vector field to evaluate SF. dr when C is the path r(t)…

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Q: Find the divergence in (2,1,-1) for the vector field FCX₁Y₁² ) = x³y² 2 ² + x ² z 3 + x^²yk

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Q: etch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line segment…

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Q: 3 2) Integrarte the vector field hlxry,2)= xyi + ya J+xa k over the twisted cubic PIt)=ti+t?g + t3 k…

A: Given that, the vector field        h(x, y, z) = xy i + yz j + xz k        r(t) = t i + t2 j + t3 k…

Q: Given the vector field F(7, y, 2) F (x, y, z) = compute the curl of F and find the values of a and…

A: curl(F)

Q: 3. Let F be the vector field (ze²z + yz², xz², xe*z + 2xyz)

A:

Q: 5. Show that F =(y cos(x),sin(x)+ y) is a conservative vector field and use this to calculate the…

A: Given: F → = y cos(x), sin(x) + y. A vector field F→ = P, Q is said to be conservative if partial…

Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

A:

Q: d) Determine whether the vector field is conservative. If it is, find a potential function for the…

A: Let a vector field is given by,                                  The vector field is conservative…

Q: Consider the following vector field: F = (y* + 1, 3ry + 1). (8.1) Is ſ. F · dr path-independent?…

A: The given vector field is F=y3+1, 3xy2+1. (8.1) For a vector field F=P,Q, the line integral ∫CF·dr…

Q: 4. Determine whether or not the vector field F(x, Y, z) = (-xye®, -xe + e° + 2y, 2z) is…

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Q: Q4. A vector field F is defined as F = psin pa,+ 2p² zas + zcos oa,. The V × F at point P(1, 7/2, 2)…

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Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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Q: 4) Consider the conservative vector field given by: F (x, y) = (y² – ye“, 2xy – e*) A potential…

A: Given vector field is F→x,y=y2−yex,2xy−ex. We have to find the potential function that generates the…

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

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 1信 -6 5 to -5+

A: We have to take point (x,y) and then draw vector field

Q: 2. Sketch the vector field F(x, y, z) = xi + yj + zk.

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Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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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: Which graph represents the gradient vector field of f(z,9) = Sz + y

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Q: Which of the following functions is a potential function for the conservative vector field F (x, y,…

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Q: Determine and state the work done by the vector field over the given path in situation. a. i. F (x,…

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Q: Show that the vector field F(x, y)= (12x² +3y² +5y)i+(6xy– 3y² +5.x)j is a conservative vector field…

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Q: (b) A potential function for the vector field F (x, y) = (2x + 1)(x² + x + 1)² 7+ (2y + 1)(y² + y +…

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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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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: Evaluate ∫C F . T ds for the vector field F = x2 i - y j along the curve x = y2 from (4, 2) to (1,…

A: Given information: The value of F=x2i+yj, x=y2 and from (4, 2) to (1, -1). Calculation: Consider…

Q: Consider the vector Field 7 and the curve C below. F(x,y) = (3 +4 ху?) 1 + 4x²yј, C is the arc of…

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Q: ermine whether the vector field F(x, y, z) = (x³, 3zy², y³) is conservative on R³. If so, find a…

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