Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.3 Dot Products - 11.3 Exercises: 36

Answer

$proj_{\textbf{v}}\textbf{u} = <0,0,0>$ $scal_{\textbf{v}}\textbf{u} = 0$

Work Step by Step

$\textbf{u} = <1,4,7>$ $\textbf{v} = <2,-4,2>$ $\textbf{u} \cdot \textbf{v} = (1)(2) + (4)(-4) + (7)(2)= 2 - 16 + 14 = 0$ $proj_{\textbf{v}}\textbf{u} = (\frac{\textbf{u} \cdot \textbf{v}}{\textbf{v} \cdot \textbf{v}})\textbf{v} = (\frac{0}{\textbf{v} \cdot \textbf{v}})<2,-4,2> = <0,0,0>$ $scal_{\textbf{v}}\textbf{u} = \frac{\textbf{u} \cdot \textbf{v}}{|\textbf{v}|} = (\frac{0}{|\textbf{v}|}) = 0$
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