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posted 2014-07-02 14:28:56 -0600

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:

$$ \langle 1,−2,3 \rangle \cdot \langle −9,−6,−1 \rangle = (1)(-9) + (-2)(-6) + (3)(-1)= -9 + 12 - 3 = 0 $$