Which one of the following choices is a plot of the vector field given by F = + T² + y? j? Select one: OB.

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: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

Q: Consider the vector field F Evaluate F · dī along the curve C: F(t) = t?i + t°j, 0<t<1

A:

Q: Make a sketch of the following vector field. F= (e-Xo) Choose the correct vector field below. O A.…

A: In the question we have to plot the curve of given vector.

Q: If F is a vector field, then É.d7 = F(B) – F(A) where the curve C goes from A to B.

A:

Q: Q19. D = yi – xJ, what is the magnitude of the vector field at the point (-1, –1)? -vz 2.

A: 19 Given vector field is V¯=yi¯−xj¯. We have to find the magnitude of the vector field at the point…

Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x,…

A:

Q: What is the value of a so that the vector field F(x.y)=(In y+2xy³) i+(ax²y2+ x/y) j is conservative?…

A: To find: the value of a for which given vector field is conservative.

Q: Which plot is defined by the vector field F given below? F(z, y) = yi + (z – y)J

A: A vector field is an assignment of a vector to each point in a subset of space.

Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax?y3+ e%)j is conservative? O…

A:

Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of x + 1…

A: Consider the given function F(x,y).

Q: The figure to the right shows a plot of a vector field F along with three curves, C1, C2, and C3.…

A:

Q: Find the field lines and sketch the field portrait for the following vector fields F : R? → R². (a)…

A: We have to sketch the field portrait for the following vector fields F→:R2→R2. a. F→x,y=xi^+x2j^b.…

Q: Q15. What would you call the vector field V = yī – xj

A:

Q: Match the following vector function with a vector field. v = 4i + x*j

A: Given vector field v= 4i + x^2 j  To plot the vector fields

Q: Determine the vector field of F. F(x, y) = 8i – 4j 1 1

A: We have given vector F=8i-4j. We have find the vector field.

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

A: We have to identify the vector field for the given vector.

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i – 3x?y?j

A:

Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

A:

Q: or not the vector field is conservative. If it is conservative, find a function f such that F cive,…

A:

Q: Which one of the following choices is a plot of the vector field given by F = -i+ Va? + y² j? +y²…

A:

Q: Make a sketch of the following vector field. F= (2y, - x) Choose the correct vector field below. O…

A: The given vector field is F=&lt;2y,-x&gt;

Q: Determine whether the vector field given by F is conservative. F(x, y) = 2xi + yj

A: Consider that any given vector field F, is said to be conservative if curl F→=0, The given function…

Q: Which graph represents the vector field F = 7i+ yj?

A: Given

Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x,…

A:

Q: Which of the below graphs is of the following vector field? F(x, y) = xi + yj

A: The vector field is a collection of points, where, each point is represented a vector quantity .  A…

Q: 4. Assume Á is a constant vector field and R = xi + yj + zk. (a) Simplify the expression (R· VR) ·…

A:

Q: Given the following vector field and orientated curve C, evaluate F-Tds. (x.y) 3/2 on the curve r(t)…

A: Given : vector field F=x, yx2+y23/2, orientable curve C with parametrization           rt=3t2, 8t2 ,…

Q: Find the gradient vector field for the function, f(z, y) = 32'y - 2zy- 1. P Rnd plot th

A:

Q: Given a vector field F(r, y) = Pi+Qj+Rk. Show that F. dr = P dr + Q dy + Rdz along a smooth curve C.

A: We have to prove that given result:

Q: If F is a vector field, then | É.d7 = F(B) – F(A) where the curve C goes from A to B.

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: |Q19. D = yi – xj, what is the magnitude of the vector field at the point (-1, –1)?

A:

Q: Which one of the following choices is a plot of the vector field given by P- F: Va2 + y? j? Va2 + y?

A:

Q: Given the following vector field and orientated curve C, evaluate F•Tds. (x.y) F = on the curve r(t)…

A:

Q: Find the curl of the vector fieldF = curl F = %3D j+ k

A:

Q: Q6) Given the following vector field: F = x?yi+ 2xy² j+ xyz k , Find V · F , V xF %3D and V· (V ×…

A:

Q: What is the value of a so that the vector field F(x.y)-(y eX+2xy4) i+(ax²y3+ e%)j is conservative? O…

A:

Q: Make a sketch of the following vector field. F= (5e%,0) Choose the correct vector field below. O A.…

A: We need to draw vector field.

Q: For the vector field F(x, y, z) = 1. a) Find curlE b) Find div E c) State whether or not the vector…

A:

Q: Given the vector field F(x,y,z)= , find the divergence and the curl of F.

A:

Q: Make a sketch of the following vector field. F= (2x.y) Choose the correct vector field below. O A.…

A: According to question, Given Vector field,F = 2x, y

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: Which one of the following choices is a plot of the vector field given by F = V? + y? j?

A:

Q: Q9. V = 2yī – xJ, what is the magnitude and direction of the vector field made with the 5, 26.6° V5,…

A:

Q: Given the following vector field and oriented curve C, evaluate F = (x,y) on the parabola r(t) =…

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: