A line has equation $r = 120 + t 2 - 1 2$ . What is the shortest distance from the point $P (4, 1, 5)$ to the line?

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What is the dot product of $a = 6 \hat{i} - 2 \hat{j} + 5 \hat{k}$ and $b = 2 \hat{i} - 2 \hat{j} - 3 \hat{k}$ ?
What is the dot product of $a = 0 \hat{i} + 0 \hat{j} - 4 \hat{k}$ and $b = 5 \hat{i} - 3 \hat{j} + 3 \hat{k}$ ?
What is the dot product of $a = 3 \hat{i} - 3 \hat{j} + 5 \hat{k}$ and $b = 4 \hat{i} + 1 \hat{j} - 2 \hat{k}$ ?
What is the dot product of $a = 2 \hat{i} - 1 \hat{j} + 5 \hat{k}$ and $b = 4 \hat{i} - 1 \hat{j} + 0 \hat{k}$ ?
What is the dot product of $a = - 1 \hat{i} + 2 \hat{j} - 2 \hat{k}$ and $b = 4 \hat{i} + 1 \hat{j} - 4 \hat{k}$ ?
What is the dot product of $a = - 4 \hat{i} + 5 \hat{j} + 5 \hat{k}$ and $b = - 2 \hat{i} + 0 \hat{j} - 3 \hat{k}$ ?