Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises: 48

Answer

(a) The scalar projection of $b$ onto $a$ is equal to the scalar projection of $a$ onto $b$ when the length of $a$ is equal to the length of $b$ or when $a$ and $b$ are orthogonal this means $a \cdot b =0$ (b) Projection of $b$ on $a$ is equal to that of $a$ on $b$ if $a =b$ or the two vectors are orthogonal. In order to this the dot product for two vectors such as $a \cdot b =0$

Work Step by Step

(a) $comp_ab=comp_ba$ when $\frac {a \cdot b}{|a|}=\frac {a \cdot b}{|b|}$ $comp_ab=comp_ba$ for $|a| = |b|$ The scalar projection of $b$ onto $a$ is equal to the scalar projection of $a$ onto $b$ when the length of $a$ is equal to the length of $b$ or when $a$ and $b$ are orthogonal this means $a \cdot b =0$ (b) $proj_ab=proj_ba$ when $\frac {a \cdot b}{(|a|)^2} \cdot a=\frac {a \cdot b}{(|b|)^2} \cdot b$ $comp_ab=comp_ba$ which happens only if $a=b$ Projection of $b$ on $a$ is equal to that of $a$ on $b$ if $a =b$ or the two vectors are orthogonal. In order to this the dot product for two vectors such as $a \cdot b =0$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.