Where did I go wrong computing the cross product

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If $u=(-2,0,\sqrt2)$ and $v=(0,-4,-\sqrt2)$, then $u\times v=(2\sqrt2,-\sqrt2,8)$.

I got $(4 \sqrt2, 2\sqrt2,0)$ for the cross product but the answer is saying I'm wrong and I don't know why

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The correct answer is that $$ (-2,0,\sqrt{2}) \times (0,-4,-\sqrt{2}) = (4\sqrt{2}, -2\sqrt{2}, 8) \,. $$ Since you have not written out your calculation, there is no way for us to know where you got it wrong.