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For a body, angular velocity \( \vec{\omega}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \) and radius
vector \( \vec{r}=\hat{i}+\hat{j}+\hat{k} \), then its velocity \( (\vec{v}=\vec{\omega} \times \vec{r}) \) is:
(1) \( -5 \hat{i}+2 \hat{j}+3 \hat{k} \)
(2) \( -5 \hat{i}+2 \hat{j}-3 \hat{k} \)
(3) \( -5 \hat{i}-2 \hat{j}+3 \hat{k} \)
(4) \( -5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}} \)
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