Let f = (z − y) i + (x − z) j + (y − x) k . let c be the rectangle of width 2 and length 5 centered at (7, 7, 7) on the plane x + y + z = 21, oriented clockwise when viewed from the origin. (a) find curlf . curlf = ⟨2,2,2⟩ (b) use stokes' theorem to find f · dr c . f · dr c = −60 √3

I suppose the rectangle's width and length refer to the dimensions of the rectangle that the plane projects onto the plane, so that and , or equivalently and .

The part of the plane bounded by can be parameterized by

with the bounds on and listed above. Call this surface . Take the normal vector to to be

a. Your answer for the curl is correct, .

b. By Stokes' theorem,

step-by-step explanation:

4  

25

5258y

54.

t5

5r

54

5856

542

5458

86

.8558.65

565

565

55898

786

8/95

5896

8656265

556478