1. The problem statement, all variables and given/known data Prove that if an object moves along any smooth simple curve C that lies on the sphere [tex]x^2 + y^2 + z^2 = a^2[/tex] in the force field [tex]F(x,y,z) = f(x,y,z)(xi + yj +zk)[/tex] where [tex]f[/tex] is a continuous function, then the work done by [tex]F[/tex] is zero. 2. Relevant equations 3. The attempt at a solution I tried to show the curl of F was zero but realized that since f can be anything it'd be impossible to show that the curl was zero, atleast i think so . Not really sure how else to approach this problem. Looking for a hint in the right direction.