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JEE Main 29-Jan-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 29-Jan-2025 Paper - Shift 14 Marks
Question
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 ____________ .
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Answer

(2)
Sol.
$\vec{\tau}=\overrightarrow{\mathbf{r}} \times \overrightarrow{\mathrm{F}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right|$
$\vec{\tau}=\hat{k}(-1-1)=-2 \hat{k}$
$|\vec{\tau}|=2 \mathrm{Nm}$

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