DUE TONIGHT I NEED HELP ASAP! Let $$ be the surface $7x9y9z=2$ in the first octant, oriented upwards. Let C be the orierted boundary of e$.$ Compute the work done in moving a unit mass particle around the boundery of a through the vector feld $F=(9x-7y)i(7y-x)j(z-9x)k$ using line integrals, and using Stotes' Theores.

Assume mass is measured in kg $,$ length in meters, and force in Newtons $(1nt=1kg-m).$

LINE INTLGRALS

Parameterise the boundary of e positively using the standard form, trup with $0t1,$ starting with the segment in the ry plane.

$C_1($the edge in the xy plane$)$ is parameterized by $$

$C_2($the edge following $C_1)$ is parameterized by $$

C$)$ the tast edge$)$ is parameterized by $$

${\displaystyle \underset{C_0}{\overset{\phantom{}}{}}}F*dr=$

${\displaystyle \underset{C_0}{\overset{\phantom{}}{}}}F*dr=$

${\displaystyle \underset{C_0}{\overset{\phantom{}}{}}}F*dr=$

${\displaystyle \underset{C_0}{\overset{\phantom{}}{}}}F*dr=$

STOKES' THEOREM

$e$ may $be$ parameterised $byr(x,y)-(x,y,f(x,y))=$

$\frac{f}{x}\frac{f}{y}-$

$-\frac{m}{m}$