May you answer this calculus $3$ question

$(i)$ The electrostatic potential, $V,in$ a region $is$ given $by$:

$V=\frac{y}{(x^2+y^2+z^2{)}^{\frac{3}{2}}}$

Suppose a unit charge $is$ located $in$ the region $at$ the point with

coordinates $(2,1,0).$ Find the direction $at$ this point, $in$ which

the rate $of$ decrease $in$ potential $is$ greatest.

$(ii)$ Find the work done $by$ the force field:

$F(x,y,z)=3$xyi$-yj+2xzk$

$in$ a moving particle around the circle $x^2+y^2=4.$

$(iii)$ Consider the vector field:

$F=y^2{z}^{3}i+2xy{z}^{3}j+3x{y}^2{z}^{2}k$

$a.$ Determine $ifFis$ conservative.

$b.IfFis$ conservative, find the corresponding potential

function $.$

$(iv)$ Consider a vector field $v$ defined $as$:

$v=(x^{2}z,2y^3{z}^2,xy{z}^2)$

Determine the divergence $of$ this vector field.

$(v)$ Show that the vector field:

$v=(xsiny,ysinx,-z(sinx+siny)).$

$is$ solenoidal.