Step 1: Divide 1275 hours by 24 to find the remainder: \[ 1275 \div 24 = 53 \, {quotient} \, {with} \, 3 \, {remainder}. \]
Step 2: The remainder 3 means the time advances by 3 hours from 9:00 p.m., which is 9:00 p.m. the next day.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?