Testing for conservative vector fields Determine whether thefollowing vector field is conservative (in ℝ2 or ℝ3). F = ⟨yex - z, ex - z, yex - z⟩

Q: 3. Find the gradient of U = 4xz² + 3yz. А. 4z3а, + 3za, + (8xz + Зу)а, В. 4z? а, + 3zay + (8xz +…

A: For a vector valued function U≡Ux,y,z, its gradient is defined as gradU=∂U∂xax+∂U∂yay+∂U∂zaz…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) | 5x*y…

A: We have to prove that differential form in the integral is exact.

Q: Sketch the vector fields. Use a table for it.    F(x,y)=<x,y-x

A: Sketch the vector field Make a table to sketch the vector field. Table should have values (x,y)

Q: vector field F = ⟨b cos(ab) + 2a + b, a cos(ab) + 2b + a⟩. State if it is conservative with reasons.

A: The given vector field If the vector field  is conservative Then

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

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: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: 77% 77%

A: Given: F(x,y) = 6i-2j

Q: Let à E R?. Let ỹ be a vector field and C be a curve. Show that V ds = . ỹ ds. ntegration of a…

A: Given that, A→∈R2 and V is a vector field. And C be a curve. The objective is to show that…

Q: Fill in the table and then sketch the vector field. z| y F(z, y) = (, %3D 20 0 2 -2 -2 2 -2 -2| -2 2…

A: Here, to fill the table and then plot the vector filed.

Q: F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?

A:

Q: Let F = 1) Find the divergence of F. V•F = 1+ 1/xz + In(y)

A:

Q: Let S be the closed surface consisting of the part of the cone x2 + y – z2 = 0 that lies between the…

A: The vector field is Fx,y,z=-x i-y j+z3 k and the surface is the part of the cone z2=x2+y2 between…

Q: Sketch representative vectors for the vector field by sketching it's scalar field. F(x, y) =…

A: Given: Vector field ,Fx,y=-12yi^+15xj^We need to sketch the scalar field using representative…

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: Let F = Find the curl of F. V×F =

A:

Q: Testing for conservative vector fields Determine whether thefollowing vector field is conservative…

A: Given: The vector field, F→=-y, xWe need to check whether the given vector field is conservative or…

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.

A:

Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr

Q: Sketch the vector field in the xy-plane. 7(7) = -7/11711³ O O y y X X O O y y X X

A: F→r→=-r→r→3

Q: a = 2xi +8zk а

A: Given to find the vector lines of the vector field  a →=2xi→+8zk→

Q: Vector Fields Slope fields are a convenient way to visualize solutions to a single differential…

A: Introduction: The vector field is very significant in understanding the nature of the solution of a…

Q: Match the vector fields: ? curl(F)=0 ? curl(F)=2 ? curl(F)=0 1. div(F)=4, 2. div(F)=0, 3. div(F)=-1,…

A: Note: As company policy, we solve first sub-parts only. Please re-submit those parts which you'd…

Q: Find the curl of the vector field F = %3D curl F = %3D

A:

Q: Match the vector field to the corresponding plot. (enter a, b, c, or d) 1. (x, y) 2. (y,x-y) 3. (y,…

A: The solution is shown below-

Q: 1. Determine the vector component of A = 3a, + 2ag – 6as tangential to the cone. %3D

A: The vector is A→=3ar+2aθ-6aϕ. Generally, the vectors are shown as sketched below:   Instead of…