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: 39

Answer

$4$, $\lt\frac{-20}{13}, \frac{48}{13}\gt$

Work Step by Step

Given: $a=\lt-5,12\gt$ , $b=\lt4,6\gt$ Scalar Projection $b$ onto $a$ can be calculated as follows: $\frac{a \times b }{|a|}=\frac{(-5 \times 4)+( 12 \times 6)}{\sqrt {(5)^{2}+(12)^{2}}}$ $=\frac{-20+72}{13}$ $=\frac{52}{13}$ $=4$ Vector Projection $b$ onto $a$ can be calculated as follows: $\frac{a \times b }{|a|^{2}}\times a=\frac{4}{13}\lt-5,12\gt$ $=\lt\frac{-20}{13}, \frac{48}{13}\gt$ Hence, Scalar Projection $b$ onto $a$ = $4$, Vector Projection $b$ onto $a$=$\lt\frac{-20}{13}, \frac{48}{13}\gt$
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