Your cross product is correct, and I see what you are trying to do with your multiplication... but you can't FOIL vectors like that. You have to use the dot product, like this:
$$ \langle 1,−2,3 \rangle \cdot \langle −9,−6,−1 \rangle = (1)(-9) + (-2)(-6) + (3)(-1)= -9 + 12 - 3 = 0 $$