If force → F = 3 ^ i + 4 ^ j - 2 ^ k acts on a particle having...

Torque in vector form is expressed as vector multiplication of position vector and force.

$\overset{\to}{τ} = \overset{\to}{r} \times \overset{\to}{F}$

⇒ \overset{\to}{τ} = \left|\begin{cases}\overset{^}{i} & \overset{^}{j} & \overset{^}{k} \\ 2 & 1 & 2 \\ 3 & 4 & - 2\end{cases}\right|

⇒ \overset{\to}{τ} = \left(- 2 - 8\right)\overset{^}{i} - \left(- 4 - 6\right)\overset{^}{j} + \left(8 - 3\right)\overset{^}{k}

⇒ \overset{\to}{τ} = \left(- 10\overset{^}{i} + 10\overset{^}{j} + 5\overset{^}{k}\right)Nm