There is a two form such that $\omega = 6dx \wedge dy+3dy \wedge dz + 2 dz \wedge dx$ and two vectors such that $V_1 = (2, 3, 1), V_2 = (2, 3, 2)$. So I have to find $\omega(V_1, V_2)$ for that I tried to split $\omega$ into some $\omega_1 \wedge \omega_2$ but I got 3 linear equations in 6 variables, which I have never done before.
$\omega_1 = a\cdot dx+b\cdot dy + c \cdot dz$ and $\omega_2 = a'\cdot dx+b'\cdot dy + c' \cdot dz$
$-ba'+ab'=6$, $-cb'+bc'=3$, $ca'-ac'=2$
It would be helpful if someone can give a step by step instruction.
and is there another way of doing this directly without splitting $\omega$?
Notice that $$(dx\wedge dy)(V_1,V_2)=dx(V_1)dy(V_2)-dx(V_2)dy(V_1)=2\cdot 3-2\cdot 3=0$$ Now do the same for the other summands in $\omega$ to get $\omega(V_1,V_2)$