Question 11 Calculate the flux of the field F across the closed plane curve C. F = xi + yj; the curve C is the counterclockwise path around the circle x2 + y2 = 9 36TT O 18TT 0 6TT

Q: F = xi + yj; the curve C is the counterclockwise path around the circle x² + y² = 16 O 8TT O 32TT 0…

A: We use Greens Theorem.

Q: Given the vector field A 4rf + 2.6rsin(0)sin(ø)0 – oo. The result of p0. The result of SA• dl along…

A: The line integral is:

Q: of the following equations would produce the direction field above

A: Given the graph is                 .

Q: Which of the figures below shows a direction field for dy x – y ? dr 5

A: We have to plot the direction field of the following differential equation: dydx=x-y5. Direction…

Q: (al Consider the 1-form w=-y dx + xdy. Sketch the corresponding vector field. Then compute the…

A: Given:a) The 1-form is  b) The vector field c) The 0-form is and the vector field To Find:a) Sketch…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

A: By using green theorem, we calculate the counterclockwise circulation and outward flux of the given…

Q: CLO 5 Consider the scalar field f=6x + 6y. The value of (curl grad f) at P(3, 1/2, N/3) is: O a 1 O…

A: Given : scalar field f=6x+6y To find : value of curl grad f at P3, π/2, π/3

Q: Inward to outward Find the exact points on the circle x2 + y2 = 2 at which the field F = ⟨ƒ, g⟩ =…

A:

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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: Calculate the flux of the field F across the closed plane curve C. F = x²i+y2j; the curve C is the…

A:

Q: CLO 5 Consider the scalar field f=5x + 6y. The value of (curl grad f) at P(3, M/2, N/3) is: а. О O…

A: The solution is given as

Q: Given the vector field A = 2rî + 7rsin(0)sin(4)ô – po. The result of , A• dl along the path "L"…

A:

Q: Prove that o curl f· dS = f pf • dr - f v o xf - d$ %3D

A:

Q: The figure here shows the vector field Vf, where f is con- tinuously differentiable in the whole…

A: From the plot of the vector field ∇f, it is clear that ∇f is constant for all points in the domain…

Q: Sketch a directional field for the equation. Identify at least 4 isoclines. dy - = y + x dx…

A: This is a problem of directional field problem.

Q: Find the curl of the vector field F curl F= (5y cos(x), 2x sin(y)).

A:

Q: The vector function r(t) = (1+2 cost) i+3j+(5 – 2 sin t) k | traces out a circle in 3-space as t…

A:

Q: The diagram is a sketch of a vector field V in the plane z= 0. The length and direction of the arrow…

A: A vector field V→ in the plane z=0 is given. The suggested function is found as shown below.