The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

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Solution

Q.
The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is __________. [2025]

Ans.
(2)

$\vec{τ} = \vec{r} \times \vec{F} =$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 1 & - 1 & 1 \end{matrix} |$

$\vec{τ} = \hat{k} (- 1 - 1) = - 2 \hat{k} \Rightarrow | \vec{τ} | = 2 Nm$

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