If \(\vec{a}\)=3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\), \(\vec{b}\)=2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\), find \(\vec{a}+\vec{b}\).

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If \(\vec{a}\)=3\(\hat{i}\)+2\(\hat{j}\)+2\(\hat{k}\), \(\vec{b}\)=2\(\hat{i}\)-8\(\hat{j}\)+\(\hat{k}\), find \(\vec{a}+\vec{b}\).