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# 09.12 - [Hand out time-sheets and group-work...

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[Hand out time-sheets and group-work work-sheet] [Collect true-false quizzes on 92.141 material] [Collect summaries of section 10.4] Section 10.3: The dot product (concluded) Important fact to keep in mind: For any vector v , we have v v = … ..?.. the length of v , squared. So | v | = sqrt( v v ). Economics example (Problem 12): A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges \$2 for a hamburger, \$1.50 for a hot dog, and \$1 for a soft drink. If A = a , b , c and P = 2, 1.5, 1 , what is the meaning of the dot product A P ? ..?.. The vendor’s revenue. Physics example: When a force-vector F causes an object to be displaced by the displacement vector D , the work

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done is … ..?.. F D (or D F ). (Note that this is negative when the angle is obtuse, or when F and D point in opposite directions; e.g., when I lower a heavy object, I’m doing negative work on it.) Suppose a b = a c , with a 0 . Can I conclude that b = c ?
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