(a) Find the angle between the surfaces $x^2 + y^2 + z^2 = 9$ and $x^…

Question

(a) Find the angle between the surfaces $x^2 + y^2 + z^2 = 9$ and $x^2 + y^2 - z = 3$ at the point $(2, -1, 2)$.

(b) Show that $\text{div}(\text{curl } \vec{F}) = 0$.

(c) Show that $\iint_S \nabla r^2 \cdot d\vec{S} = 6V$, where $r = |\vec{r}|$, $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ and $S$ is a closed surface enclosing a volume $V$.

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