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: 34

Answer

$proj_{\textbf{v}}\textbf{u} = <0,-6,3>$ $scal_{\textbf{v}}\textbf{u} = \frac{-15}{\sqrt 5}$

Work Step by Step

$\textbf{u} = <5,0,15>$ $\textbf{v} = <0,4,-2>$ $\textbf{u} \cdot \textbf{v} = (5)(0) + (0)(4) + (15)(-2)= 0 + 0 - 30 = -30$ $\textbf{v} \cdot \textbf{v} = (0)(0) + (4)(4) + (-2)(-2) = 0 + 16 + 4 = 20$ $|\textbf{v}| = \sqrt {(0)^2 + (4)^2 + (-2)^2} = 2\sqrt {5}$ $proj_{\textbf{v}}\textbf{u} = (\frac{\textbf{u} \cdot \textbf{v}}{\textbf{v} \cdot \textbf{v}})\textbf{v} = (\frac{-30}{20})<0,4,-2> = <0,-6,3>$ $scal_{\textbf{v}}\textbf{u} = \frac{\textbf{u} \cdot \textbf{v}}{|\textbf{v}|} = (\frac{-30}{2\sqrt {5}}) = \frac{-15}{\sqrt 5}$
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