Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.2 - Vectors - Exercises 12.2 - Page 704: 24

Answer

See image. Instructions are below.

Work Step by Step

$a.$ Translate the vector ${\bf -v}$ so it starts where$ {\bf u}$ terminates. Join the start of ${\bf u}$ with the end of ${\bf -v}$. $b.$ Translate the vector ${\bf w}$ so it starts where $ {\bf u-v}$ terminates. Join the start of ${\bf u-v}$ with the end of ${\bf w}$. $c.$ Translate the vector ${\bf -v}$ so it starts where $ {\bf 2u}$ terminates. Join the start of ${\bf 2u}$ with the end of ${\bf -v}$. $d.$ Translate the vector ${\bf v}$ so it starts where $ {\bf u}$ terminates. Join the start of ${\bf u}$ with the end of ${\bf v} $to obtain ${\bf u+v}$. Now, translate ${\bf u+v}$ so it starts where ${\bf w}$ ends. The resultant vector starts and ends at the same point. The result is the zero vector.
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