To understand two different techniques for computing the torque on an object due to an applied force. imagine an object with a pivot point p at the origin of the coordinate system shown (figure 1). the force vector f⃗ lies in the xy plane, and this force of magnitude f acts on the object at a point in the xy plane. the vector r⃗ is the position vector relative to the pivot point p to the point where f⃗ is applied. the torque on the object due to the force f⃗ is equal to the cross product τ⃗ =r⃗ ×f⃗ . when, as in this problem, the force vector and lever arm both lie in the xy plane of the paper or computer screen, only the z component of torque is nonzero. when the torque vector is parallel to the z axis (τ⃗ =τk^), it is easiest to find the magnitude and sign of the torque, τ, in terms of the angle θ between the position and force vectors using one of two simple methods: the tangential component of the force method or the moment arm of the force method. note that in this problem, the positive z direction is perpendicular to the computer screen and points toward you (given by the right-hand rule i^×j^=k^), so a positive torque would cause counterclockwise rotation about the z axis.