Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 12 - Section 12.3 - The Dot Product - 12.3 Exercises - Page 854: 64

Answer

If $(u+v) $ and $(u-v)$ are orthogonal this implies $(u+v) \cdot (u-v)=0$, then the vectors $u$ and $v$ must have the same length.

Work Step by Step

$(u+v) $ and $(u-v)$ are orthogonal when $(u+v) \cdot (u-v)=0$ $u \cdot u-u.v+v.u-v.v=0$ $u.u-v.v=0$ Since,$u.u=|u|^2$ Thus, $|u|^2=|v|^2$ Hence, it has proved that if $(u+v) $ and $(u-v)$ are orthogonal this implies that $(u+v) \cdot (u-v)=0$; thus the vectors $u$ and $v$ must have the same length.
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