If force F → = 3 i ^ + 4 j ^ - 2 k ^ acts on a particle having position vector 2 i ^ + j ^ + 2 k ^ then, the torque about the origin will be:

Question

If force F &#8594; = 3 i ^ + 4 j ^ - 2 k ^ acts on a particle having position vector 2 i ^ + j ^ + 2 k ^ then, the torque about the origin will be:

Aicharya · Accepted Answer

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

$\vec{τ} = \vec{r} \times \vec{F}$

$\Rightarrow \vec{τ} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 2 \\ 3 & 4 & - 2 \end{matrix}|$

$\Rightarrow \vec{τ} = (- 2 - 8) \hat{i} - (- 4 - 6) \hat{j} + (8 - 3) \hat{k}$

$\Rightarrow \vec{τ} = (- 10 \hat{i} + 10 \hat{j} + 5 \hat{k}) N m$

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