Problem 1.15 Calculate the divergence of the following vector functions:
Problem 118 Calculate the curls of the vector functions in Prob. 1.15 We were unable to transcribe this image
Find the divergence of the following vector field:
Find the divergence Find the divergence of the following vector field: E = x+_y + _z where b is a constant + r
Calculate the divergence and curl of the vector V = (- 4.9)(rz cos2(θ)) er + (- 6.8)(sin2(θ) + rz) eθ + ( 5.8)(rz + sin(θ)) ez at the point P ≡ ( 6.1, 0.4, - 4.3). (Round your answer to 2 decimal places.) Calculate the divergence and curl of the vector v = (- 4.9)(rz cos-(0)) e, +(-6.8) (sin (0) + rz) eg +(5.8) (rz + sin()) ez at the point P =( 6.1, 0.4. - 4.3). (Round your answer...
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)
Use the divergence theorem to calculate the flux of the vector field \(\vec{F}(x, y, z)=x^{3} \vec{i}+y^{3} \vec{j}+z^{3} \vec{k}\) out of the closed, outward-oriented surface \(S\) bounding the solid \(x^{2}+y^{2} \leq 16,0 \leq z \leq 3\).
7. Calculate the divergence over the volume of a sphere of radius 3 in a vector field where =4rsin- cos.(r, with Deduce the flux through the surface of the sphere. 7. Calculate the divergence over the volume of a sphere of radius 3 in a vector field where =4rsin- cos.(r, with Deduce the flux through the surface of the sphere.
1.15. Show the following vector identities by writing each vector in terms of Cartesian unit vectors and showing that each component of the LHS is equal to the corresponding component of the RHS. (a) a·(bxc)=c·(axb)=b·(cxa)
Problem 1.26 Prove that the divergence of a curl is always zero. Check it for function Va in Prob. 1.15 We were unable to transcribe this image
Find the divergence of the following vector field. F = (4yz sin x, 9xz cos y, xy cos z) The divergence of F is