Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 55



Work Step by Step

Projection of $\textbf{u}$ along $\textbf{v}=\textbf{u}_{||\textbf{v}}$$=(\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||^{2}})\textbf{v}$ $\textbf{u}\cdot\textbf{v}=⟨-1,2,0⟩\cdot ⟨2,0,1⟩=-1\times2+2\times0+0\times1=-2$ $||\textbf{v}||^{2}=(\sqrt {2^{2}+0^{2}+1^{2}})^{2}=2^{2}+1^{2}=5$ Then, $\textbf{u}_{||\textbf{v}}=(-\frac{2}{5})\,⟨2,0,1⟩=⟨-\frac{4}{5},0,-\frac{2}{5}⟩$
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