If $\vec{a}=3\hat{i}-2\hat{j}+4\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$, then:
(a) Find $\vec{a} \times \vec{b}$.
(b) Find $(\vec{a} \times \vec{b}) \cdot \vec{a}$ and verify that $\vec{a} \times \vec{b} \perp \vec{a}$.
(c) Find $(\vec{a} \times \vec{b}) \cdot \vec{b}$ and verify that $\vec{a} \times \vec{b} \perp \vec{b}$.