Explain Torque in vector from.

Explanation

(i) The torque of a force about an axis is independent of the choice of the origin as long as it is chosen on that axis itself.
(ii) Let O be the origin on the axis AB, wich is the rotational axis of a rigid body. F is the force acting at the point P. Now, choose another point O' anywhere on the axis.
(iii) The torque of F about O' is
`bar(O'P) xx vec(F) = (bar(O'O) + bar(OP)) xx vec(F)`
`= (bar(O'O) xx vec(F)) + (bar(OP) xx vec(F))`
(iv) As `bar(O'O) xx vec(F)` is perpendicular to `bar(O'O)`, this term will not have a component along AB. Thus, the component of `bar(O'P) xx vec(F)` is equal to that of `bar(OP) xx vec(F)`