What is the shortest distance between the lines $r = (i + 3 k) + s (2 i + j + 2 k)$ and $r = (- 3 i - 2 j + 2 k) + t (2 i - 3 j - 2 k)$ ?

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What is the dot product of $a = 4 \hat{i} + 4 \hat{j} + 0 \hat{k}$ and $b = 2 \hat{i} + 3 \hat{j} - 1 \hat{k}$ ?
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