Explain how the torque can be expressed as a vector product of two vectors ? How the direction and magnitude of torque is determined ?

Explanation

(i) For direction, the vector rule or right hand rule is used.
`tau = r F sin theta`
(ii) The expression for the magnitude of torque can be written in two different ways by associating `sin theta` either with r of F in the following manner.
`{:(tau = r (F sin theta) = r xx (F bot)),(tau = (r sin theta) F = (r bot) xx F):}`
(iii) Here, `(F sin theta)` is the component of `vec(F)` perpendicular to `vec(r)`. Similarly, `(r sin theta)` is the component of `vec(r)` perendicular to `vec(F)`