Solving Stokes Problem with Circle and Vector Field - Help with Homework

[amk1995]

Homework Statement

Find ∫CF⃗ ⋅dr⃗ where C is a circle of radius 2 in the plane x+y+z=3, centered at (2,4,−3) and oriented clockwise when viewed from the origin, if F⃗ =5yi⃗ −5xj⃗ +4(y−x)k⃗

Homework Equations

Stokes theorem.

∫curl F ⋅dS

The Attempt at a Solution

For the curl I get <4,4,-10>
For dS I get <1,1,1> from z = 3-x-y
Dotted together its -2
so

-2∫∫dA
Area of circle is 4∏

-8∏ is my answer but online homework system says it's not… Please help!

 

[LCKurtz]

Homework Statement

Find ∫CF⃗ ⋅dr⃗ where C is a circle of radius 2 in the plane x+y+z=3, centered at (2,4,−3) and oriented clockwise when viewed from the origin, if F⃗ =5yi⃗ −5xj⃗ +4(y−x)k⃗

Homework Equations

Stokes theorem.

∫curl F ⋅dS

The Attempt at a Solution

For the curl I get <4,4,-10>
For dS I get <1,1,1> from z = 3-x-y
Dotted together its -2
so

-2∫∫dA
Area of circle is 4∏

-8∏ is my answer but online homework system says it's not… Please help!

I get the same as you did.