The point $Q (5, 2, 4)$ is reflected in the straight line $r = (1, 0, - 1) + t (1, 2, 2)$ . The image point is

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