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: 40

Answer

$\frac{14}{\sqrt {17}}$, $\lt\frac{14}{17}, \frac{56}{17}\gt$

Work Step by Step

Given: $a=\lt1,4\gt$ , $b=\lt2,3\gt$ Scalar Projection $b$ onto $a$ can be calculated as follows: $\frac{a \times b }{|a|}=\frac{(1 \times 2)+( 4 \times 3)}{\sqrt {(1)^{2}+(4)^{2}}}$ $=\frac{2+12}{\sqrt {17}}$ $=\frac{14}{\sqrt {17}}$ Vector Projection $b$ onto $a$ can be calculated as follows: $\frac{a \times b }{|a|^{2}}\times a=\frac{14}{17}\lt1,4\gt$ $=\lt\frac{14}{17}, \frac{56}{17}\gt$ Hence, Scalar Projection $b$ onto $a$ = $\frac{14}{\sqrt {17}}$, Vector Projection $b$ onto $a$=$\lt\frac{14}{17}, \frac{56}{17}\gt$
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