What are the conditions in which force can not produce torque ?

Explanation

The torque is zero with `vecr` and `vecF` are parallel or antiparallel. If parallel then `theta=0^(@)` and `sin 0^(@)=0`. If antiparallel, then `theta=180^(@)` and `sin 180^(@)=0`. Hence `tau=0`
The torque is zero if the force acts at the reference point. i.e. as `vecr=0, tau=0`.