If $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{3j}-\overrightarrow{2k}$ and $\overrightarrow{b}=\overrightarrow{-i}+\overrightarrow{3k}$ than find $\overrightarrow{a}\times\overrightarrow{b}$. Verify that $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to$\overrightarrow{a}\times\overrightarrow{b}$ separately.

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