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 - Page 853: 46


$\lt \frac{20}{17},\frac{-5}{17} \gt$

Work Step by Step

By definition: $proj_ab=\frac{ab}{|a|^2}a$ $a = \lt 1,4 \gt, b= \lt 2,3 \gt$ $a \cdot b= 1 (2)+4 (3)=14$ $|a|= \sqrt {17}$ and $|a|^2=17$ $proj_ab=\frac{ab}{|a|^2}a$ $=\frac{14}{17}\lt 1,4 \gt$ $=\lt \frac{14}{17},\frac{56}{17} \gt$ $orth_a{b}=b-proj_ab$ $=\lt 2,3 \gt-\lt \frac{14}{17},\frac{56}{17} \gt$ $=\lt 2-\frac{14}{17},3-\frac{56}{17} \gt$ $=\lt \frac{20}{17},\frac{-5}{17} \gt$
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