Word Count : 324

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### Part (a): Evaluate \( \bar{\triangledown} \times (r^3 \vec{r}) \) We need to compute the curl of \( r^3 \vec{r} \), where: - \( r = |\vec{r}| = \sqrt{x^2 + y^2 + z^2} \), - \( \vec{r} = x\hat{i} + y\hat{j} + z\hat{k} \), - \( r^3 \vec{r} = r^3 (x\hat{i} + y\hat{j} + z\hat{k}) \). The curl operator in Cartesian coordinates is: \[ ______ _______ ________ ____ ____ _______ _________ __________ _______ ______ ______ _____.
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