The problem that I am unsure about is: k x (i - 2j). What are the rules for adding and subtracting vectors like this?
Be careful about notation, in particular capitalization.
I think you mean: $\displaystyle k\times(i-2j)~?$
The rules are: $\displaystyle \vec{a}\times(\vec{b}+\vec{c})=(\vec{a}\times\vec{ b})+(\vec{a}\times\vec{c})$ and $\displaystyle (\alpha\vec{ a}\times\vec{b})=\alpha(\vec{a}\times\vec{b})$