These vectors can be represented as $\vec{A} = a_{i}\hat{i} + a_{j}\hat{j} + a_{k}\hat{k}$ and $\vec{B} = b_{i}\hat{i} + b_{j}\hat{j} + b_{k}\hat{k}$, where $a_{i}, a_{j}, a_{k}, b_{i}, b_{j}, b_{k}$ are the components of the vectors in the $\hat{i}, \hat{j},
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