Chapter 15 - Section 15.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises - Page 838: 22

$0$

Work done $=\int_a^b F(r(t)) \dfrac{dr}{dt}(dt)$ and $ \dfrac{dr}{dt}=\cos t i-\sin t j +\dfrac{1}{6} k$ Then work done $=\int_0^{2 \pi} \cos t -\cos^2 t\sin t+2 \sin t dt$ or, $=[\sin t+(1/3) cos^3 t-2 \cos t ]_0^{2 \pi}$ or, $=0$