As an exercise, I was trying to compute the interior product as follows.
Given $\alpha=z^2dx\wedge dy$ and $\beta=xdx\wedge dy\wedge dz$ and $X=y\frac{\partial}{\partial x}-x\frac{\partial}{\partial y}$. Compute $\iota_X\alpha$ and $\iota_X\beta$.
I have gotten the following results $\iota_X\alpha=yz^2dy+xz^2dx$ and $\iota_X\beta=xydy\wedge dz+x^2dx\wedge dz$, but since there is no way for me to verify that this results are correct I just wanted to share them to see if someone can tell me if they are indeed correct. Thanks