Question

Find the torque of a force `(7 hati + 3hatj - 5hatk)` about the origin. The force acts on a particle whose position vector is `(hati - hatj + hatk)`.

Answer 1

Here,`oversetrarr(F) = 7hati + 3hatj - 5hatk, - overset rarr(r ) = hati - hatj + hatk`
`overset rarr(tau) = overset rarr(r ) xx overset rarr(F) = (hati - hatj + hatk) xx (7hati + 3hatj - 5hatk)`
`= |[hati,hatj,hatk],[1,-1,+1],[7,+3,-5]|`
`oversetrarr(tau) = hati (5 - 3) - hatj (-5 - 7) + hatk (3 + 7)`
`overset rarr(tau) = 2hati + 12 hatj + 10hatk`