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

Explanation

`vecr=hati-hatj+hatkandvecF=7hati+3hatj-5hatk`
`vectau=vecrxxvecF`
`=(hati-hatj+hatk)xx(7hati+3hatj-5hatk)`
`=|(hati,hatj,hatk),(1,-1,1),(7,3,-5)|`
`=hati[(-1)(-5)-(3)(1)]-hatj[(1)(-5)-(7)(1)]`
`+hatk[(1)(3)-(7)(-1)]`
`=hati[5-3]-hatj[-5-7]+hatk[3+7]`
`vectau=2hati+12hatj+10hatk`
Magnitude of `vectau`,
`tau=sqrt((2)^(2)+(12)^(2)+(10)^(2))`
`=sqrt(4+144+100)`
`=sqrt(248)`
`~~15.75` unit