Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 666: 42


$$(u+v)\cdot(u- v)= -8.$$

Work Step by Step

We have $$(u+v)\cdot(u- v)=u\cdot u-u\cdot v+v\cdot u-v\cdot v=\| u\|^2-\| v\|^2\\ = 1^2-3^2=1-9=-8.$$
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