Question

What should be the angle between the direction of force and the direction of motion of a body so that the work done is zero?

Answer 1

The relation between work, force, distance and angle between the two is:
W = (F) (S) cos θ
Where,
(W) - Work done
(F) - Force
(S) - Displacement
(θ) - Angle between force and displacement
When the force is perpendicular to the direction of motion,   and hence, the work done is also zero.
Example - The work done by the earth on a satellite moving in a circular orbit around it is zero.