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A spacecraft at $\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ is subjected to a force $\lambda \hat{\mathrm{k}}$ by firing a rocket. The spacecraft is subjected to a moment of magnitude
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$\sqrt{5} \lambda$
$\begin{aligned} & \vec{\tau}=\vec{r} \times \overrightarrow{\mathrm{F}}=(\hat{i}+2 \hat{j}+3 \hat{k}) \times \lambda \hat{k} \\ &=2 \lambda \hat{i}-\lambda \hat{j} \\ \Rightarrow &|\vec{\tau}|=\sqrt{5} \lambda \end{aligned}$
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