Use Stokes' Theorem to evaluate

Question

C
F · dr
where C is oriented counterclockwise as viewed from above.
F(x, y, z) = xyi + 5zj + 7yk,
C is the curve of intersection of the plane
x + z = 8
and the cylinder
x2 + y2 = 9.

Answer 1

You doing an MITx subject?

Answer 2

Just asking :)

Answer 3

curve is ellipse
at z = 11 and 5, y = 0 and x = +/-3
(-3 , 0 , 11)
(+3 , 0, 5)

at z = 8 , x = 0 and y = +/-3
The normal to that ellipse is in he x z plane and is perpendicular to the line joining(-3, 0 ,11)and (3,0,5)
slope of that original line dz/dx =
-6/6 = -1
remarkable
so slope of our normal is dz/dx = 1

N = 1 i + 0 j + 1k

Now maybe you can do F dot N

Answer 4

or rather curl F