Use the definitions of divergence and curl to establish the vector identities a: ∇ * ( F x G ) = G * ( ∇ x F ) - F * ( ∇ x G) b: ∇ x ( fG ) = ( ∇f x G) + ( f∇ x G ) Use the definitions of divergence...

Question

Question

Use the definitions of divergence and curl to establish the vector identities

a: ∇ * ( F x G ) = G * ( ∇ x F ) - F * ( ∇ x G)

b: ∇ x ( fG ) = ( ∇f x G) + ( f∇ x G )

math calculus

Answer 1

Answer #1

a) Consider | F G) Ti-FXG In scalar triple product the cross and dot can be inter changed Ox Ox aG of

Answer 2

Similar Homework Help Questions

7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)=...

7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)= e' sin yi+e' cos yj+zk F.de where is the curve of intersection of the plane : = 5 - x and the cylinder rº + y2 = 9. 8. Use Stokes Theorem to evaluate F(x, y, - ) = xyi +2=j+3yk
Curl and Divergence of a Vector Field

How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
Find the divergence and curl of the vector field

Find the divergence and curl of the vector field \(\vec{F}=y^{2} z^{3} \hat{x}+x y \hat{y}+\left(5 z^{2}+y\right) \hat{z}\)

Find the divergence and curl of the vector field

Find the divergence and curl of the vector field \(\vec{F}=5sin\theta\hat{r}\)
answer asap Find the curl and the divergence of the vector field: F = 4x71 +...

answer asap Find the curl and the divergence of the vector field: F = 4x71 + 2xy j - 4xz k
Find the divergence and curl of the vector field

Find the divergence and curl of the vector field \(\vec{F}=2 \cos \phi \hat{s}+\frac{z}{s} \hat{z}\)

6. Find the divergence and the curl of the vector field F(x,y,z) = 4xy'i+ xej+xyek. 6....

6. Find the divergence and the curl of the vector field \(\mathbf{F}(x, y, z)=4 x y^{2} \mathbf{i}+x e^{4 z} \mathbf{j}+x y e^{-4 z} \mathbf{k}\)
Find the divergence and curl of the vector field s20

Find the divergence and curl of the vector field \(\vec{F}=s^{\frac{1}{2}} \hat{\phi}\)s20
(a) Prove that the divergence of a curl is always zero for any vector field. (b)...

(a) Prove that the divergence of a curl is always zero for any vector field. (b) Prove that the curl of the gradient of a scalar function is always zero.

(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...

(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2) Let F(x, y, z) = (2exz, 3 sin(xy), x7y2z6). (a) Find the divergence of F. (b)Find the curl of F. -/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...