II -3 -3 -3 II 3 IV 3 11 -3 3. 3.

Q: Which plot is defined by the vector field F given below? F(2, v) = zi – uj Select one: 2 -2 -4 -2 2…

A: The correct answer is option 'd' . Since, F(x,y)= xi - yj  And if we put the point like (x,0) , then…

Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,y) Choose the correct answer below. O…

A: Make a table by considering some points and form from and to points as shown in step 2. Then plot…

Q: Sketch the vector field F= (2,3y) Choose the correct answer below. O A. O B. OC. OD.

A: Solve

Q: Which of the following vector fields matches the plot below? -2 -1 1 -D1 -2 1 F(2, y) = i - 7 %3D 1…

A: Given the vector filed,  To match the vector field with the given plot.

Q: g (x, y) = 5x² + 3xy + y² find the conservative vector field.

A: We know that  a conservative vector field is also a gradient vector. So here we will use this…

Q: Determine the vector field of F. F(x, y) = 4i – 2j

A: To find the vector field F .

Q: Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j +…

A:

Q: Does the vector field plotted below appear to be conservative? 1.0 0.5- 0.0- %3D -0.5 -1.0b -1.0…

A: Graphically, a vector field is conservative if it has no tendency to ``swirl around.'' If it did…

Q: Find the gradient vector field of the function f. f(x, у, 2) 3 3x соs Vf(x, у, 2) %3D

A:

Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

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

A: step 2 complete solution

Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

A:

Q: Determine the vector field of F. F(r, y) = yi -

A: Solution:

Q: Determine if the vector field F=(yz,xz,xy) is conservative?

A:

Q: Determine the vector field of F. F(r, y) = 4i – 2j

A: To determine the vector field F .

Q: Determine the vector field of F. F(x, y) %3D 6і — 3j

A: Solution :-

Q: Match the vector fields F with the plots labeled I-IV. Give reasons for your choices. F(x, y) = ⟨y,…

A: Vector field of function represents the vector corresponding to each point of the given function. To…

Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2 j+ Cx z°I where the coefficients A, B,…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2j+ Cx tk, %3D where the coefficients A,…

A:

Q: Sketch the vector field F= (5,4y) Choose the correct answer below. O A. OB. OC.

A:

Q: Select the plot of the vector field F(z, y) = (2, z). %3D

A: Given vector field is F(x, y) = (2, x)

Q: Find the gradient vector field Vf of fand sketch it, for f(x, y) = x2 - y.

A:

Q: Find the streamlines of the vector field and the streamline through the given point. F(x, y, z) =i+…

A:

Q: F(x.y) = (4xy, - 3y²> A V.F- 4x B VF-1 © v.F = 4x - 6y (D vi--2y

A:

Q: F=(P(x.y).Q(x. y).0) Find when the Vector field F is conservative.

A:

Q: Find the gradient vector field of f(x, y, z) = e 9z+8y+2z < e9 e8 e2 Question Help: M Message…

A:

Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

A:

Q: 1. For each of the following vector fields F(1, y), decide if there is function f(z, y) such that F…

A:

Q: Find ||FI|. F(x, y) = yi + xj Sketch several representative vectors in the vector field. y C -2 2 2…

A: given vector fieldF(x, y)=yi+xj

Q: 3. Let f: R2 → R be the function which satisfies for all (x, y) E R² that f(x, y) = 100 – x² – 2y?…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: Determine the vector field of F. F(x, y) = 6i – 3j

A:

Q: What is the value of a so that the vector field F(x.y)=(y eX+4xy³) i+(ax²y4+ eX)j is conservative? O…

A:

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

A: Concept:

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: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,4y) Choose the correct answer below. O…

A:

Q: Find a potential function for the vector field F(r, y) = (22ry + 11y- 3, 11z? + 11r). f( x, y) =…

A:

Q: Determine the vector field of F. F(x, y) = 6i – 2j

A: The general form of a vector-valued function in two dimensions is given by F=F1i+F2j, where F1 and…

Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

A: consider the following

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

A: GIVEN : F (x, y, z) = xi + yj + zk Explanation: A vector field is a function F that assigns to each…

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

A:

Q: Determine the vector field of F. F(x, y) = 81-4)

A: The given vector is F=8i-4j

Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

A:

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

A:

Q: 9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ…

A: The general form of a vector valued function in three dimensions is given by…

Q: Sketch a sample of vectors for the vector field F(x, y) = (3x y) Choose the correct answer below.…

A: The solution are next step

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (3, -9, 7)…

A:

Q: Determine the vector field of F. F(x, y) = 9i – 3j

A:

Q: Sketch the vector field F= (6,4y) Choose the correct answer below. OA. B.

A: The given vector field is F=&lt;6,4y&gt; The Plot of the vector field is

Q: Choose the option in which the vector field is conservative. Select one: F =(xy,x+y> F = (2xy² -…

A:

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: