The force acting on a particle `vecr=(4,6,12)m` of a rigid body is `vecF=(6,8,10)N`. Find the magniude of the torque producing the rotational motion. Axis of rotation is along the unit vector `(1)/(sqrt(3))(1,1,1)`.

Explanation

`vectau=vecrxxvecF`
The magnitude of the torque with respect to the axis on which the unit vector is `hatn` is
`vec(tau_(n))=(vecrxxvecF).hatn`
`therefore vecrxxvecF=|(hati,hatj,hatk),(4,6,12),(6,8,10)|`
`therefore vecrxxvecF=hati(60-96)-hatj(40-72)+hatk(32-36)`
`=-36hati+32hatj-4hatk=(-36hati+32hatj-4hatk)Nm`
`therefore` Magnitude of the torque responsible for rotational motion
Now, `(vecrxxvecF).hatn=(-36,32,-4).(1)/(sqrt(3))(1,1,1)`
`=(1)/(sqrt(3))(-36+32-4)`
`therefore vec(tau_(n)).hatn=-(8)/(sqrt(3))Nm`
`therefore tau=(8)/(sqrt(3))Nm`