Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 6 - Exercises and Problems - Page 105: 19


The proof is below.

Work Step by Step

We prove that the two results are the same. We will use a two-dimensional vector to prove this. (Ai+Bj)((Ci+Dj)+(Ei+Fj)) We add the two first and then expand: (Ai+Bj)((C+E)i+(D+F)j) We use the definition of the dot product to find: (AC+AE)+(BD+BF) We now use the distributive property to prove this is an equivalent method: (Ai+Bj)((Ci+Dj)+(Ei+Fj)) (Ai)(Ci+Dj)+Ai(Ei+Fj)+Bj(Ci+Dj)+Bj(Ei+Fj) Simplifying gives: AC+AE+BD+BF This is the same result as above.
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