A particle of mass m is acted upon by a force at a point P whose position vector with respect to the origin O is r.
a. (i) Define the physical quantity "torque" about the origin produced by the force.
b. (ii) Describe, with the aid of the right-hand rule, how the sense (direction) of this torque vector is decided.
c. (iii) Prove that the magnitude of the torque is given by τ=rFsinθ, where θ is the angle between r and the force vector F. State clearly the geometrical meaning of sinθ that appears in this relation.