Find the divergence and curl of the vector field \(\vec{F}=5sin\theta\hat{r}\)
Find the divergence and curl of the vector field \(\vec{F}=2 \cos \phi \hat{s}+\frac{z}{s} \hat{z}\)
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 \(\vec{F}=s^{\frac{1}{2}} \hat{\phi}\)s20
How do I find the curl and divergence of the vector field F(x,y,z) = {1/√(x2+y2+z2)}*(xi +yj+zk) ?
answer asap Find the curl and the divergence of the vector field: F = 4x71 + 2xy j - 4xz k
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
(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.
Solve with all the steps please! Calculate the divergence and the curl of the vector field F(x,y,z) = ( x^3y)i + (xy)j + ( 213 )k. (Where Fis a vector and i,j,k stand for the standard unit vectors)
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 curl of the vector. Find the curl of the following vector field: t-y where b is a constant and r = x-+y +z