How to express $\omega$ as linear combination of wedge products?

Question

I know that $$\omega \begin{bmatrix}a\\b\\c\end{bmatrix},\begin{bmatrix}d\\e\\f\end{bmatrix}=3ae-2af-3bd+4bf+2cd-4ce$$ How would I write this as a linear combination of: $dx\wedge dy$, $dx\wedge dz$, and $dy\wedge dz$ ?

Answer 1

HINT: What do you get when you evaluate each of $dx\wedge dy$, $dx\wedge dz$, and $dy\wedge dz$ on your pair of vectors?