Question

Find the torque of a force `(5 hati - 2 hatj + 3 hatk)` about the origin, which acts on a particle whose position vector is `( hati - hatj + hatk)`.

Answer 1

`overset rarr(F) = (5 hati - 2 hatj + 3hatk)` and `= (hati - hatj + hatk)`
`overset rarr(tau) = overset rarr(r ) xx overset rarr(F) = (hati - hatj + hatk) xx (5hati - 2hatj + 3 hatk)`
`= |[hati, hatj, hatk],[1,-1,1],[5,-2,3]|`
`= hati (-3 + 2) - hatj (3 - 5) + hatk(-2 + 5)`
`= (-hati + 2hatj + 3hatk)`