The divergence of x2coszi⃗ +ylogxj⃗ −yzk⃗ 𝑥2𝑐𝑜𝑠𝑧𝑖→+𝑦𝑙𝑜𝑔𝑥𝑗→−𝑦𝑧𝑘→ is 0Select one:TrueFalse

The divergence of the vector field F⃗ =(x+3y)i^+(y−3z)j^+(x−2z)k^𝐹→=(𝑥+3𝑦)𝑖^+(𝑦−3𝑧)𝑗^+(𝑥−2𝑧)𝑘^ isa.None of theseb.0c.2d.-2

In the region of free space that includes the volume 2 < x,y,z < 3.D = [ (2y/z)ax + (2x/z)ay - (4xy/z2)az) ] C/m2(i) Evaluate the volume integral side of the divergence theorem for the volumedefined by 2 < x,y,z < 3

Electric Flux Density is independent of material properties: Justify/Contradict.In the region of free space that includes the volume 2 < x,y,z < 3.D = [ (2y/z)ax + (2x/z)ay - (4xy/z2)az) ] C/m2(i) Evaluate the volume integral side of the divergence theorem for the volumedefined by 2 < x,y,z < 3

The volume of the sphere x2+y2+z2=1𝑥2+𝑦2+𝑧2=1 is evaluated by:a.4∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy4∫01∫01−𝑦21−𝑥2−𝑦2𝑑𝑥𝑑𝑦b.8∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy8∫01∫01−𝑦21−𝑥2−𝑦2𝑑𝑥𝑑𝑦c.8∫10∫101−x2−y2−−−−−−−−−√dxdy8∫01∫011−𝑥2−𝑦2𝑑𝑥𝑑𝑦d.16∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy

Let  ϕ(x,y,z)=3x2y−y3z2.𝜙(𝑥,𝑦,𝑧)=3𝑥2𝑦−𝑦3𝑧2. Then the gradient of ϕ𝜙 at (1,1,0) isa.6i^−3j^+0k^6𝑖^−3𝑗^+0𝑘^b.None of thesec.6i^+3j^+0k^6𝑖^+3𝑗^+0𝑘^d.6i^+6j^+0k^6𝑖^+6𝑗^+0𝑘^Clear my choice