Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check for agreement. F= (z-y,x, -x); 2 2 D = {(x,y,z2); + +1} y 9 12 8 2

Q: 4.) Verify the Expansion of the triple vector product A x (B x ) = B⋅ (A·C) - C (A. B) by direct…

A:

Q: Let A(5, -1, -3) and B(1, 3, 2) be two points in R. The directional derivative of f(x, y, z) = xy…

A:

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Evaluate ∫C F. d r for the vector field F = y i - x j counterclockwise along the unit circle x2 + y2…

A: Evaluate ∫_C F. d r for the vector field F = y i - x j counterclockwisealong the unit circle x2 + y2…

Q: What is the flux through the described surface?

A: The surface is described by The vector field is F=<1, 3x, 2y>To evaluate the Flux for the…

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: 2. For the vector field V = (7x³ + 2y2²)i + (4x²z - 7y²+3)j + (4y³ +2² -32²) k find the divergence…

A:

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: Determine the vector field of FF. F(x,y)=8i−4j

A: Solution

Q: S f(x) dx = 5 ve 8(y) dy = 7 olsun. R = [0,2] × [2,3] olacak şekilde %3D %3D I = SSrf(x)g(y) dA…

A: To find the solution of double integral.

Q: Find the curl of the vector field F. F = (x-y+z)i+ (6x-y+7z)j+ (9x +6y + z)k curl F = i+

A: We have to find the curl F

Q: y X Consider the vector field u(x) = x²+²x² + y²j+6k. i Calculate y dr, where C is the straight line…

A: Introduction:  A line integral is an integral where the function to be integrated is evaluated along…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A:

Q: Select the irrotational vector field. O A yz î-2xz + xyz k O B. yz î + xz î + xz R OCzî + z2 + yz R…

A:

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

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 3. Let F and G be vector fields with differentiable components. Express curl (F x G) in term of div…

A: Introduction: The curl of a vector is a vector-valued function. It is the cross-product of the…

Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

A:

Q: Show that 0 x a =0 = a x 0 for any vector a in V3

A: lets take vectorv=(x,y,z) and   0=(0,0,0)

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A:

Q: Compute the curl of the vector field F = -4zi - 5y 3-4x k. =url= =

A: Given,  The Vector Field,F→=-4zi-5yj-4xk The Curl of the vector field is to be calculated.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: Suppose S is the surface where x² + y² + 3z² = 1. Let F be the vector field F = (xy, yz, z²).…

A: We need to evaluate integral.

Q: Sketch the following vector fields (at least 10 vectors) (a) F(x, y) =

A: Consider the provided question, 7 (a)

Q: re f an -2, 3)

A:

Q: Find the curl of the vector fleld F(z, y, 2) = zi+ 8'y=²j+2rk. Enter your answer in standard unit…

A: