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 - Preliminary Questions - Page 666: 3


Distributive property.

Work Step by Step

If $ v $ is orthogonal to $ u $ and $ w $, then we have $$ v\cdot u=0, \quad v\cdot w=0.$$ Now, $ v\cdot (u+w)=v\cdot u+v\cdot w=0$, which means that $ v $ is orthogonal to $ u+w $. Hence, we use the distributive property.
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