JEE MAIN - Physics (2025 - 22nd January Evening Shift - No. 3)
The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be
$\hat{j}+\hat{k}$
$\hat{i}-\hat{k}$
$\hat{i}-\hat{j}+\hat{k}$
$\hat{i}+\hat{k}$
Explanation
$\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 1 & 1 & 1 \\ 2 & 1 & 2\end{array}\right|=\hat{\mathrm{i}}-0 \hat{\mathrm{j}}-\hat{\mathrm{k}}$
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