Consider the vector field $X=x \partial_{x}+y \partial_{y}+z \partial_{z}$, the two-form $\alpha=2 z d x \wedge d y+$ $3 y d x \wedge d z$, and the three-form $\omega=d x \wedge d y \wedge d z$ on $\mathbb{R}^{3}$. Calculate

(i) $i_{X} \alpha$,

(ii) $i_{X} \omega$,

(iii) $\mathcal{L}_{X} \alpha$.